Álgebra/Tema 5 Teorema del Binomio ER_A1_C2_01_M Suma geométrica ER_A1_C2_01_M

Calcule la siguiente suma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»1«/mn»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»3«/mn»«/msup»«mo»+«/mo»«mo»§#8943;«/mo»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>max</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>14</mn><mo>-</mo><mi>a</mi><mo>-</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mo>(</mo><mo>-</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>b</mi></munderover><mo>(</mo><mo>-</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mo>(</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>b</mi></munderover><mo>(</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14707</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14706</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19607</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19608</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_02_M Suma de a_n=an+b ER_A1_C2_02_M

Considere la sucesión de números reales definida por: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/math», con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math».

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mo»#«/mo»«mi»S«/mi»«mn»2«/mn»«/mrow»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>p</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>p</mi></msub><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S2</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>c</mi></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>b</mi><mo>+</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>c</mi></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><ms>a</ms><mi>i</mi></msub></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>66</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cont</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_03_F Multiplicación de a_n ER_A1_C2_03_F

Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«/math» una sucesión de números reales dada por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math»

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>k</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>b</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>c</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>d</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mo>-</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mo>-</mo><mi>sol3</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>192</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>192</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_04_M Multiplicación de a_n ER_A1_C2_04_M

Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«/math» una sucesión de números reales dada por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«/mrow»«/msup»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math»

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mi»p«/mi»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/munderover»«msub»«mi»a«/mi»«mi»p«/mi»«/msub»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>&gt;</mo><mn>2</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>k</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mi>c</mi></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mi>c</mi></mrow><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2048</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1048576</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16384</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_06_D Suma multiplicativa ER_A1_C2_06_D

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»v«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/munderover»«mi»c«/mi»«mo»§#183;«/mo»«mi»k«/mi»«mo»§#183;«/mo»«mi»k«/mi»«mo»!«/mo»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>k</mi></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>i</mi></mrow><mrow><mi>v</mi><mo>=</mo><mi>j</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>a</mi></mrow><mi>b</mi></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>b</mi><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1451424</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>161184</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1451516</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>161276</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mn>7</mn></apply></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5040</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ExpC2P10 - A-Matemática Discreta-M-Suma telescópica ExpC2P10

Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msubsup»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/msubsup»«mo»[«/mo»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«mo»-«/mo»«mo»#«/mo»«mi»f«/mi»«mn»2«/mn»«mo»]«/mo»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>32</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>b1</mi><mo>&gt;</mo><mo>(</mo><mi>a1</mi><mo>+</mo><mn>8</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>sen</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mn>1</mn><mo>/</mo><mi>x</mi><mo>,</mo><mo>&nbsp;</mo><mi>exp</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>log</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mfrac><mn>1</mn><msup><mi>x</mi><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></msup></mfrac><mo>,</mo><msqrt><mi>x</mi></msqrt><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i1</mi><mo>=</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>f1</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>b1</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>-</mo><mi>fun</mi><mo>(</mo><mi>a1</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>f1</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>-</mo><mi>fun</mi><mo>(</mo><mi>b1</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>sen</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>}</mo></math></input></command></group></library><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mfenced><mi>x</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>a1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.84385</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>j</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>x</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>&nbsp;</mo><mo>,</mo><mi>fun</mi><mo>(</mo><mi>b1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>12</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>30</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>19</mn><mn>372</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0.65364</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P11 - A-Matemática Discreta-M-Sumatorias dobles ExpC2P11

Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/munderover»«mo»§#160;«/mo»«mo»§#160;«/mo»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/munderover»«mo»#«/mo»«mi»c«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/mrow»«/msup»«mspace linebreak=¨newline¨/»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>x1</mi><mo>=</mo><mn>1</mn></mrow><mi>a1</mi></munderover><munderover><mo>∑</mo><mrow><mi>x2</mi><mo>=</mo><mn>1</mn></mrow><mi>x1</mi></munderover><mo>(</mo><mi>c1</mi><msup><mo>)</mo><mrow><mi>x1</mi><mo>+</mo><mi>x2</mi></mrow></msup></math></input></command></group></library><library closed="true"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/><assertion name="check_integer_form"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-0)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P3 - 2.2 Matemática Discreta-M-Sumatoria y sus propiedades ExpC2P3

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mfrac»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«mo»*«/mo»«msup»«mi»k«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»f«/mi»«mn»2«/mn»«mo»*«/mo»«mi»k«/mi»«mo»#«/mo»«mi»f«/mi»«mn»3«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>25</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><msup><mi>p</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>p</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>-</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mn>1</mn><mo>-</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mn>1</mn><mi>p</mi></mfrac><mo>*</mo><mfenced><mrow><mo>-</mo><mfrac><mn>1</mn><mrow><mi>p</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>-</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>p</mi><mo>*</mo><mi>m</mi><mo>-</mo><mn>1</mn></mrow></mfrac></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>144</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>18</mn><mn>64357</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P4 - 2.2.1 A-Matemática Discreta-Suma telescopica-D ExpC2P4

Calcule el valor de la siguiente suma  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mo»#«/mo»«mi»k«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»k«/mi»«mo»!«/mo»«/mrow»«mrow»«mo»#«/mo»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>u</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>v</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>!</mo><mo>-</mo><mi>a</mi><mo>!</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P5 - 2.2.1 A-Matemática Discreta-Sumatorias-M ExpC2P5

Calcule el valor de las siguiente suma  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»h«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»u«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»w«/mi»«mn»1«/mn»«/mrow»«/munderover»«mfrac»«mrow»«mo»#«/mo»«mi»e«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»h«/mi»«mn»1«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»g«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»h«/mi»«mn»1«/mn»«mo»+«/mo»«mn»1«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>u1</mi><mo>+</mo><mn>4</mn><mo>,</mo><mi>u1</mi><mo>+</mo><mn>9</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>g1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>mcd</mi><mo>(</mo><mi>e1</mi><mo>,</mo><mi>g1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>&nbsp;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mn>1</mn><mi>g1</mi></mfrac><munderover><mo>∑</mo><mrow><mi>h1</mi><mo>=</mo><mi>u1</mi></mrow><mi>w1</mi></munderover><mo>(</mo><msup><mfenced><mfrac><mi>e1</mi><mi>g1</mi></mfrac></mfenced><mi>h1</mi></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>&nbsp;</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3376</mn><mn>19683</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>253318912</mn><mn>4782969</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>799744</mn><mn>59049</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P6 - 2.2/2.3 - Matemática Discreta - M - Productoria con suma telescópica ExpC2P6

Calcule el valor de la siguiente productoria:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»#«/mo»«msup»«mi»p«/mi»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»e«/mi»«mi»l«/mi»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mi>m</mi><mo>+</mo><mn>3</mn><mo>,</mo><mi>m</mi><mo>+</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>si</mi><mo>&nbsp;</mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>1</mn><mo>&nbsp;</mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>&quot;</mo><msup><mi>k</mi><mn>2</mn></msup><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><msup><mi>p</mi><mfrac><mrow><mi>n</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>-</mo><mo>(</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>m</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>6</mn></mfrac></msup></mtd></mtr><mtr><mtd><mi>fin</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>si</mi><mo>&nbsp;</mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>2</mn><mo>&nbsp;</mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>k</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><msup><mi>p</mi><mrow><mo>-</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mi>m</mi></mfrac></mrow></msup></mtd></mtr><mtr><mtd><mi>fin</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>si</mi><mo>&nbsp;</mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>3</mn><mo>&nbsp;</mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>&quot;</mo><mn>2</mn><mi>k</mi><mo>-</mo><mn>1</mn><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><msup><mi>p</mi><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><msup><mi>m</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></msup></mtd></mtr><mtr><mtd><mi>fin</mi></mtd></mtr></mtable></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3794275180128377091639574036764685364535950857523710002444946112771297432041422848</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P7 - 2.3 Matemática Discreta-F-Productoria y sus propiedades ExpC2P7

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»#«/mo»«msup»«mi»p«/mi»«msup»«mi»k«/mi»«mn»2«/mn»«/msup»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mi>m</mi><mo>+</mo><mn>3</mn><mo>,</mo><mi>m</mi><mo>+</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><msup><mi>p</mi><mrow><mfrac><mrow><mi>n</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>6</mn></mfrac><mo>-</mo><mfrac><mrow><mo>(</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>m</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>6</mn></mfrac></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>88537996291958256446260440678593208943077817551131498658191653913030830300434060998128233014667</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P8 - A-Matemática Discreta-M-Propiedades de pitatorias (con sumatoria) ExpC2P8

Calcule:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/munderover»«mfenced open=¨[¨ close=¨]¨»«mrow»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/mrow»«/munderover»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»)«/mo»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>}</mo></mrow><mrow><mi>x1</mi><mo>≠</mo><mi>x2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>b1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>x2</mi><mo>=</mo><mi>b1</mi></mrow><mi>c1</mi></munderover><mfenced close="]" open="["><mrow><munderover><mo>∑</mo><mrow><mi>x1</mi><mo>=</mo><mn>1</mn></mrow><mi>x2</mi></munderover><mfenced><mrow><mi>d1</mi><mo>+</mo><mi>e1</mi><mo>*</mo><mi>x1</mi></mrow></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30225</mn></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="times_operator">·</option><option name="tolerance">10^(-1)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P9 - A-Matemática Discreta-M-Suma geométrica ExpC2P9

Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msubsup»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/msubsup»«mo»[«/mo»«mfrac»«mrow»«mo»(«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mo»]«/mo»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>32</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>b1</mi><mo>&gt;</mo><mo>(</mo><mi>a1</mi><mo>+</mo><mn>8</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr></mtable><mrow><mi>d1</mi><mo>≠</mo><mi>c1</mi><mo>&nbsp;</mo><mo>&amp;</mo><mo>&nbsp;</mo><mi>e1</mi><mo>≠</mo><mi>c1</mi><mo>&amp;</mo><mi>d1</mi><mo>≠</mo><mi>e1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>x1</mi><mo>=</mo><mi>a1</mi></mrow><mi>b1</mi></munderover><mo>(</mo><mfrac><mrow><mo>(</mo><msup><mi>c1</mi><mi>x1</mi></msup><mo>)</mo><mo>+</mo><mo>(</mo><msup><mi>d1</mi><mi>x1</mi></msup><mo>)</mo></mrow><mrow><mo>(</mo><msup><mi>e1</mi><mi>x1</mi></msup><mo>)</mo></mrow></mfrac><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_1 Sumatorias Calcule el resultado de la sumatoria:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»i«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«mrow»«msup»«mo»)«/mo»«mi»i«/mi»«/msup»«mo»)«/mo»«/mrow»«/math»

]]> 1.0000000 0.3333333 0 0 #n - 12(1+(-1)#n+1)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>16</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>n</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>(</mo><mn>1</mn><mo>+</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mo>#</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_2 Sumatorias Calcule el valor total de la sumatoria:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»i«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«msup»«mi»i«/mi»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 2×#n3+3×#n2+#n]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>&#215;</mo><mo>#</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><mo>&#215;</mo><mo>#</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mo>#</mo><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_3 Sumatorias Calcule el valor de la sumatoria siguiente:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»#«/mo»«msup»«mi»a«/mi»«mrow»«mi»k«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 (#a#n-1)/(#a-1)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>#</mo><msup><mi>a</mi><mrow><mo>#</mo><mi>n</mi></mrow></msup><mo>-</mo><mn>1</mn><mo>)</mo><mo>/</mo><mo>(</mo><mo>#</mo><mi>a</mi><mo>-</mo><mn>1</mn><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_4 Sumatorias Calcule el valor de la sumatoria siguiente:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»(«/mo»«msup»«mi»k«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #n3×1/3+#n2×1/2+#n/6-#a×#n]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>13</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><msup><mi>n</mi><mn>3</mn></msup><mo>&#215;</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>+</mo><mo>#</mo><msup><mi>n</mi><mn>2</mn></msup><mo>&#215;</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mo>#</mo><mi>n</mi><mo>/</mo><mn>6</mn><mo>-</mo><mo>#</mo><mi>a</mi><mo>&#215;</mo><mo>#</mo><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sumas-AL-F-Calcular una suma Calcule el valor de la siguiente suma  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mo»#«/mo»«msup»«mi»k«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>22</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>58</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>&lt;</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>a</mi></mrow><mi>b</mi></munderover><msup><mi>k</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_4 Sumatoria de Multiplos Determina la suma de los multiplos de #a que se encuentren entre #b y #c (sin considerar estos dos numeros)

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mo>=</mo><mi>b</mi></mrow><mrow><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mi>a</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iinicial</mi><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>suma</mi><mo>=</mo><mi>suma</mi><mo>+</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mi>a</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ifinal</mi><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>suma</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iinicial</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>104</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ifinal</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1776</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_5 Sumatoria de Potencias Encuentre la suma de las potencias de #a que se encuentren entre #b y #c (sin incluir estos dos últimos):

]]> 1.0000000 0.3333333 0 0 #suma <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>50</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>contador</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mi>b</mi></mrow><mtable><mtr><mtd><mi>i</mi><mo>=</mo><msup><mi>a</mi><mi>contador</mi></msup></mtd></mtr><mtr><mtd><mi>contador</mi><mo>=</mo><mi>contador</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>i</mi><mo>=</mo><msup><mi>a</mi><mi>contador</mi></msup></mtd></mtr><mtr><mtd><mi>suma</mi><mo>=</mo><mi>suma</mi><mo>+</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>contador</mi><mo>=</mo><mi>contador</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mi>suma</mi><mo>-</mo><mi>i</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>350</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6900</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15625</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>contador</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3750</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#suma</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_7 Sumatorias «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»e«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»{«/mo»«mo»§#160;«/mo»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«mo»§#160;«/mo»«mo»}«/mo»«mo»§#160;«/mo»«mi»l«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»u«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mi»i«/mi»«mi»§#243;«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»i«/mi»«mi»d«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»o«/mi»«mi»r«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mi»n«/mi»«/msup»«mo»§#160;«/mo»«mo»,«/mo»«mn»1«/mn»«mo»§#8804;«/mo»«mi»n«/mi»«mo»§#8804;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mo»(«/mo»«mi»n«/mi»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»n«/mi»«mo»§#62;«/mo»«mo»#«/mo»«mi»b«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mi»a«/mi»«mi»l«/mi»«mi»c«/mi»«mi»u«/mi»«mi»l«/mi»«mi»e«/mi»«mo»§#160;«/mo»«munderover»«mrow»«mo»§#8721;«/mo»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«/mrow»«mrow»«mi»n«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mo>(</mo><mo>-</mo><mi>a</mi><msup><mo>)</mo><mi>n</mi></msup><mo>+</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></mrow><mi>c</mi></munderover><mo>(</mo><mi>n</mi><mo>+</mo><mi>a</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>35299463</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_8 Sumatoria Parcial Calcule la suma parcial de los #n primeros términos de una progresión aritmética cuyo primer término es #a y su diferencia es #d

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>634</mn><mo>,</mo><mn>1321</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>29</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>29</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2538</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58018680</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 5 Teorema del Binomio/Revisar ER_A1_C2_03_F Multiplicación de a_n ER_A1_C2_03_F

Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«/math» una sucesión de números reales dada por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math»

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>k</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>b</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>c</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>d</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mo>-</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mo>-</mo><mi>sol3</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>192</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>192</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_05_D Suma telescópica ER_A1_C2_05_D

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»v«/mi»«mo»=«/mo»«mo»#«/mo»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«/mrow»«mrow»«mo»#«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«/mrow»«/munderover»«mfenced»«mrow»«msqrt»«mo»#«/mo»«mi»v«/mi»«/msqrt»«mo»-«/mo»«msqrt»«mo»#«/mo»«mi»v«/mi»«mo»+«/mo»«mn»2«/mn»«/msqrt»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>13</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>k</mi></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>i</mi></mrow><mrow><mi>v</mi><mo>=</mo><mi>j</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msqrt></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msqrt></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msqrt></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msqrt></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msqrt><mn>13</mn></msqrt><mo>+</mo><msqrt><mn>26</mn></msqrt><mo>-</mo><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>5</mn><mo>*</mo><msqrt><mn>13</mn></msqrt><mo>-</mo><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>17</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question>