Álgebra/Tema 2 Inducción, Sumatoria y Productoria/Control 2 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>></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> </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> </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> </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> 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»

«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>×</mo><mo>#</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><mo>×</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:

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]]> 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> 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»