Álgebra/Tema 2 Inducción, Sumatoria y Productoria/Medio 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

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"><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>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><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></mtd></mtr><mtr><mtd><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><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>"</mo><msub><mi>a</mi><mi>n</mi></msub><mo>"</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>"</mo><msub><mi>a</mi><mi>i</mi></msub><mo>"</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>"</mo><msub><mi>a</mi><mi>j</mi></msub><mo>"</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>"</mo><msub><mi>a</mi><mi>p</mi></msub><mo>"</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>S2</mi><mo>=</mo><mo>"</mo><msub><mi>a</mi><mi>k</mi></msub><mo>"</mo></mtd></mtr><mtr><mtd><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></mtd></mtr><mtr><mtd><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></mtd></mtr><mtr><mtd><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></mtd></mtr><mtr><mtd><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></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>sol1</mi><mo>≠</mo><mi>sol3</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>sol1</mi><mo>≠</mo><mi>sol4</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>sol1</mi><mo>≠</mo><mi>sol2</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>sol2</mi><mo>≠</mo><mi>sol4</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>sol3</mi><mo>≠</mo><mi>sol4</mi></mrow></apply></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>p</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>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>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>3</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>7</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>95</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>119</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>128</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>59</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><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>></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>"</mo><msub><mi>a</mi><mi>n</mi></msub><mo>"</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>"</mo><msub><mi>a</mi><mi>k</mi></msub><mo>"</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>"</mo><msub><mi>a</mi><mi>i</mi></msub><mo>"</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>"</mo><msub><mi>a</mi><mi>j</mi></msub><mo>"</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> 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> </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> </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> </mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>1</mn><mo> </mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>"</mo><msup><mi>k</mi><mn>2</mn></msup><mo>"</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> </mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>2</mn><mo> </mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>"</mo><mfrac><mn>1</mn><mrow><mi>k</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>"</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> </mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>3</mn><mo> </mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>"</mo><mn>2</mn><mi>k</mi><mo>-</mo><mn>1</mn><mo>"</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> 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>></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> </mo><mo>&</mo><mo> </mo><mi>e1</mi><mo>≠</mo><mi>c1</mi><mo>&</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> </mo><mo>-</mo><mo> </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_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>×</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>+</mo><mo>#</mo><msup><mi>n</mi><mn>2</mn></msup><mo>×</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>×</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>