Álgebra/Tema 7: Teorema del Binomio Teorema del Binomio: Buscar el r-ésimo término del desarrollo Encuentre el término que está en la «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«msup»«mn»1«/mn»«mi»a«/mi»«/msup»«/math» posición del binomio:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

Desarrolle en la forma: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mi»a«/mi»«mo»+«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mi»n«/mi»«/msup»«mo»=«/mo»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»0«/mn»«/mrow»«mi»n«/mi»«/munderover»«mfenced»«mtable»«mtr»«mtd»«mi»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«msup»«mi»a«/mi»«mrow»«mi»n«/mi»«mo»-«/mo»«mi»k«/mi»«/mrow»«/msup»«msup»«mi»b«/mi»«mi»k«/mi»«/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>a1</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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></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>x</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>p</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>=</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>y</mi><mo>,</mo><mi>a</mi><mo>→</mo><mi>b</mi><mo>,</mo><mi>m</mi><mo>→</mo><mi>n</mi><mo>,</mo><mi>u</mi><mo>→</mo><mi>v</mi><mo>,</mo><mi>r</mi><mo>→</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>→</mo><mi>q</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>R1</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x1</mi><mo>+</mo><mfrac><mi>y1</mi><mi>a2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</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>a1</mi><mo>*</mo><mi>x1</mi><msup><mo>)</mo><mrow><mi>n1</mi><mo>-</mo><mi>r1</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mfenced><mfrac><mi>y1</mi><mi>a2</mi></mfrac></mfenced><mrow><mi>r1</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n1</mi><mrow><mi>r1</mi><mo>-</mo><mn>1</mn></mrow></apply></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>a</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</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"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</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"><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>-</mo><mfrac><mn>1</mn><mn>12</mn></mfrac><mo>*</mo><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</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"><mfrac><mn>455</mn><mn>509508050791800359789246182327659329346961478229047145136128</mn></mfrac><mo>*</mo><msup><mi>a</mi><mn>3</mn></msup><mo>*</mo><msup><mi>b</mi><mn>57</mn></msup></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> Teorema del binomio: determinar el valor de una constante bajo ciertas condiciones El valor de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»§#8712;«/mo»«msup»«msub»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»0«/mn»«/msub»«mo»+«/mo»«/msup»«/math» tal que los coeficientes de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»X«/mi»«mn»1«/mn»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»X«/mi»«mn»2«/mn»«/math» sean iguales en el desarrollo de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

es:

]]> 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><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Variable</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>binomio</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>r</mi><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Exponentes</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>numerador</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>denominador</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>binomio</mi><mo>:</mo></math></comment></maction><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>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Exponente</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>desarrollo</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Expresión</mi><mo>&nbsp;</mo><mi>binomial</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>está</mi><mo>&nbsp;</mo><mi>bajo</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>exponente</mi><mo>&nbsp;</mo><mi>n1</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mrow><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>2</mn></mrow></msup></mrow><mi>a</mi></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>3</mn></mrow></msup></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>rs1</mi><mo>&nbsp;</mo><mi>son</mi><mo>&nbsp;</mo><mi>objetos</mi><mo>&nbsp;</mo><mi>para</mi><mo>&nbsp;</mo><mi>obtener</mi><mo>&nbsp;</mo><mi>frs1</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>conjunto</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>exponentes</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>tiene</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>variable</mi><mo>&nbsp;</mo><mi>x1</mi><mo>&nbsp;</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>en</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>desarrollo</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>binomio</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>lista</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rs1</mi><mo>=</mo><mi>recorrido</mi><mo>(</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>frs1</mi><mo>=</mo><mo>{</mo><mi>a1</mi><mo>*</mo><msub><mi>s1</mi><mi>i</mi></msub><mo>-</mo><mi>a2</mi><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><msub><mi>s1</mi><mi>i</mi></msub><mo>)</mo><mo>&nbsp;</mo><mi>con</mi><mo>&nbsp;</mo><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>rs1</mi><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Exponentes</mi><mo>&nbsp;</mo><mi>positivos</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>binomio</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Posfrs1</mi><mo>=</mo><mo>{</mo><mi>x</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>frs1</mi><mo>&nbsp;</mo><mi>donde</mi><mo>&nbsp;</mo><mi>x</mi><mo>&gt;</mo><mn>0</mn><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Términos</mi><mo>&nbsp;</mo><mi>sobre</mi><mo>&nbsp;</mo><mi>los</mi><mo>&nbsp;</mo><mi>cuales</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>hace</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>pregunta</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>el</mi><mo>&nbsp;</mo><mi>enunciadio</mi><mo>&nbsp;</mo><mi>con</mi><mo>&nbsp;</mo><mi>respectivos</mi><mo>&nbsp;</mo><mi>k</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>min</mi><mo>(</mo><mi>Posfrs1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X1</mi><mo>=</mo><msup><mi>x1</mi><mi>y1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mfrac><mrow><mi>y1</mi><mo>+</mo><mi>a2</mi><mo>*</mo><mi>n1</mi></mrow><mrow><mi>a1</mi><mo>+</mo><mi>a2</mi></mrow></mfrac></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>m1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y2</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>k1</mi><mo>+</mo><mi>m1</mi><mo>)</mo><mo>-</mo><mi>a2</mi><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mi>k1</mi><mo>-</mo><mi>m1</mi><mo>)</mo></mtd></mtr></mtable><mrow><mi>y2</mi><mo>&lt;</mo><mi>a1</mi><mo>*</mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><mi>k1</mi><mo>+</mo><mi>m1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X2</mi><mo>=</mo><msup><mi>x1</mi><mi>y2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Solución</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mfenced><mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n1</mi><mi>k2</mi></apply><mo>*</mo><msup><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n1</mi><mi>k1</mi></apply><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfenced><mfrac><mn>1</mn><mi>m1</mi></mfrac></msup></math></input></command></group></library><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"><mfrac><msup><mi>y</mi><mn>4</mn></msup><mi>a</mi></mfrac><mo>-</mo><mfrac><mn>1</mn><msup><mi>y</mi><mn>4</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>MinPosfrs1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>MinPosfrs1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</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>X1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>+</mo><mi>k1</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>y2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</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>m1</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>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>77</mn></msqrt><mn>10</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> Teorema del binomio: encontrar el coeficiente de un término específico El coeficiente de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»r«/mi»«mn»1«/mn»«/mrow»«/msup»«/math» en el desarrollo de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

 es:

]]> 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>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>w</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><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mfrac><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow><mrow><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a1</mi><mo>&lt;</mo><mn>1</mn><mo>∧</mo><mi>a2</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a2</mi><mo>≠</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>∩</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>longitud</mi><mo>{</mo><mo>}</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</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">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Teorema del Binomio: expresar una suma como un binomio elevado a un cierto término menos un resto 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»«mo»#«/mo»«mi»k«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/munderover»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/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>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>}</mo></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>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>r</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>a1</mi><mo>=</mo><mfenced><mfrac><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></mfrac></mfenced></mrow><mrow><mi>a1</mi><mo>∉</mo><integers/></mrow></apply></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"><mi>sol</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>a1</mi><msup><mo>)</mo><mi>y1</mi></msup><mo>-</mo><munderover><mo>∑</mo><mrow><mi>l</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>k1</mi><mo>-</mo><mn>1</mn></mrow></munderover><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>y1</mi><mi>l</mi></apply><mo>*</mo><msup><mi>a1</mi><mi>l</mi></msup></math></input></command></group></library><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"><msup><mfrac><mn>3</mn><mn>5</mn></mfrac><mi>k</mi></msup></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><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>!</mo><mo>+</mo><mn>5</mn><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>!</mo><mo>*</mo><msup><mfrac><mn>8</mn><mn>5</mn></mfrac><mi>t</mi></msup><mo>-</mo><mn>5</mn><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>!</mo></mrow><mrow><mn>5</mn><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>!</mo></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>!</mo><mo>=</mo><mn>6</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></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> VA_AI_15 Teorema del Binomio Calcular el quinto término en el desarrollo de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«/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>expresion1</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>3</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>3</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>4</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>4</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>5</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>5</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>6</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>6</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expresion2</mi><mo>=</mo><mo>{</mo><msup><mfenced><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>3</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>3</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>4</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>4</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>5</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>5</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>6</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>6</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><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"><mi>sol</mi><mo>=</mo><mn>70</mn></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>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expfinal</mi><mo>=</mo><msub><mi>expresion1</mi><mi>b</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>expresion1</mi><mi>b</mi></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>expresion2</mi><mi>b</mi></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>16</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>14</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>12</mn></msup><mo>+</mo><mn>56</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>10</mn></msup><mo>+</mo><mn>70</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>8</mn></msup><mo>+</mo><mn>56</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>6</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>4</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>8</mn></msup></mfrac></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_16 Teorema del Binomio 2 Encuentre el coeficiente de

#termino1

en el desarrollo de

#desarrollo

 

]]> 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>termino</mi><mo>=</mo><mo>{</mo><msup><mi>x</mi><mn>11</mn></msup><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><msup><mi>x</mi><mn>5</mn></msup><mo>,</mo><mo>&quot;</mo><msup><mi>x</mi><mrow><mn>2</mn><mi>r</mi></mrow></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>desarrollo0</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mn>7</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mroot><mi>x</mi><mn>3</mn></mroot><mo>-</mo><mfrac><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></mrow></mfenced><mn>27</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mfrac><mn>3</mn><mi>x</mi></mfrac></mrow></mfenced><mn>13</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mrow><mn>4</mn><mi>r</mi></mrow></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi><mo>=</mo><mo>{</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>7</mn><mn>4</mn></apply><mo>*</mo><msup><mn>2</mn><mn>4</mn></msup><mo>*</mo><msup><mn>3</mn><mn>3</mn></msup><mo>,</mo><mo>-</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>27</mn><mn>3</mn></apply><mo>*</mo><msup><mn>2</mn><mn>3</mn></msup><mo>,</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>13</mn><mn>4</mn></apply><mo>*</mo><msup><mn>2</mn><mn>9</mn></msup><mo>*</mo><msup><mn>3</mn><mn>4</mn></msup><mo>,</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mrow><mn>4</mn><mi>r</mi></mrow><mrow><mn>2</mn><mi>r</mi></mrow></apply><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>termino1</mi><mo>=</mo><msub><mi>termino</mi><mi>b</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>desarrollo</mi><mo>=</mo><msub><mi>desarrollo0</mi><mi>b</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>resultado</mi><mi>b</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>termino1</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>resultado</mi><mn>4</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>4</mn><mo>*</mo><mi>r</mi></mrow></mfenced><mo>!</mo></mrow><mrow><mfenced><mrow><mn>2</mn><mo>*</mo><mi>r</mi></mrow></mfenced><msup><mo>!</mo><mn>2</mn></msup></mrow></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> VA_AI_17 T.B. Término Central Encontrar el término central en el desarrollo de:

#expre

]]> 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>expr</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><mfrac><mn>3</mn><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>5</mn><mi>a</mi></mrow><mn>6</mn></mfrac></mrow></mfenced><mn>10</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mfrac><mrow><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>5</mn></mfrac><mo>-</mo><mfrac><mn>5</mn><mrow><mn>2</mn><mi>x</mi></mrow></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msqrt><mrow><mi>a</mi><mo>-</mo><mi>x</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></msqrt></mrow></mfenced><mn>24</mn></msup><mo>;</mo><mo>&nbsp;</mo><mn>0</mn><mo>&lt;</mo><mi>x</mi><mo>&lt;</mo><mi>a</mi><mo>⩽</mo><mi>b</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mroot><mi>x</mi><mn>3</mn></mroot><mo>-</mo><mfrac><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mn>2</mn></mfrac></mrow></mfenced><mn>6</mn></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resul</mi><mo>=</mo><mo>{</mo><mo>-</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>10</mn><mn>5</mn></apply><mo>*</mo><mo>(</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><msup><mo>)</mo><mn>5</mn></msup><mo>*</mo><msup><mi>a</mi><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>,</mo><mn>1120</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>,</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>24</mn><mn>12</mn></apply><mo>*</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>x</mi><msup><mo>)</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mi>k</mi></mrow><mn>2</mn></mfrac></msup><mo>*</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>k</mi><msup><mo>)</mo><mfrac><mi>k</mi><mn>2</mn></mfrac></msup><mo>,</mo><mo>-</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>6</mn><mn>3</mn></apply><mo>*</mo><msup><mn>2</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>*</mo><msup><mi>x</mi><mrow><mo>-</mo><mn>15</mn></mrow></msup><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>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expre</mi><mo>=</mo><msub><mi>expr</mi><mi>a</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>resul</mi><mi>a</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expre</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><msqrt><mrow><mi>a</mi><mo>-</mo><mi>x</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></msqrt></mrow></mfenced><mn>24</mn></msup><ms>;</ms><mo>&nbsp;</mo><ms>0&lt;x&lt;a</ms><mo>⩽</mo><ms>b</ms></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>2704156</mn><mo>*</mo><msup><mfenced><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mrow><mo>-</mo><mfrac><mi>k</mi><mn>2</mn></mfrac><mo>+</mo><mn>12</mn></mrow></msup><mo>*</mo><msup><mfenced><mrow><mi>b</mi><mo>-</mo><mi>k</mi></mrow></mfenced><mfrac><mi>k</mi><mn>2</mn></mfrac></msup></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> VA_AI_18 T.B. Término Independiente Encuentre el termino independiente de x en el desarrollo de

#form

]]> 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><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mi>x</mi></mrow></mfrac></mrow></mfenced><mn>9</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></mrow></mfenced><mrow><mn>3</mn><mi>n</mi></mrow></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>{</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>9</mn><mn>6</mn></apply><mo>*</mo><mfrac><mn>1</mn><msup><mn>6</mn><mn>3</mn></msup></mfrac><mo>,</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mi>n</mi></msup><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mrow><mn>3</mn><mi>n</mi></mrow><mi>n</mi></apply><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>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>form</mi><mo>=</mo><msub><mi>a</mi><mi>c</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>b</mi><mi>c</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>form</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></mrow></mfenced><mrow><mn>3</mn><mi>n</mi></mrow></msup></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><mrow><mfenced><mrow><mn>3</mn><mo>*</mo><mi>n</mi></mrow></mfenced><mo>!</mo><mo>*</mo><msup><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mi>n</mi></msup></mrow><mrow><mfenced><mrow><mn>2</mn><mo>*</mo><mi>n</mi></mrow></mfenced><mo>!</mo><mo>*</mo><mi>n</mi><mo>!</mo></mrow></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> VA_AI_19 T.B. Término Específico Encuentre, si es que existe, el término que contenga al factor x2y45 en el desarrollo del binomio

(2x3y-1 - x-2y4)25

OBS: En caso de no existir, escribir una p.

]]> 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>sol</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>25</mn><mn>14</mn></apply><mo>*</mo><msup><mn>2</mn><mn>11</mn></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>9128755200</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> VA_AI_20 T. Binomio (Ecuación) Determine el valor de x en los Naturales que satisface la siguiente ecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mtable»«mtr»«mtd»«mi»x«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»+«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»x«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»c«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»d«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»c«/mi»«/mtd»«/mtr»«/mtable»«/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>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>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>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>b</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>b</mi></math></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"/><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_21 T. Binomio (Coeficientes) Determine la suma de los coeficientes de los dos términos centrales en el desarrollo del binomio:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»#«/mo»«mi»x«/mi»«mi»a«/mi»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»b«/mi»«mo»#«/mo»«mi»x«/mi»«mi»b«/mi»«mo»)«/mo»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»n«/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>a</mi><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>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>2</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">while</csymbol><mrow><mi>b</mi><mo>=</mo><mo>=</mo><mn>0</mn></mrow><mrow><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>,</mo><msqrt><msup><mi>x</mi><mn>3</mn></msup></msqrt><mo>,</mo><mroot><mi>x</mi><mn>5</mn></mroot><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xb</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><msup><mi>x</mi><mn>3</mn></msup><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><mfrac><mn>1</mn><msup><mi>x</mi><mn>2</mn></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>n</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pregunta</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>xa</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>xb</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coef1</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n</mi><mfrac><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mn>2</mn></mfrac></apply><mo>*</mo><msup><mi>a</mi><mfrac><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mn>2</mn></mfrac></msup><mo>*</mo><msup><mi>b</mi><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coef2</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n</mi><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac></apply><mo>*</mo><msup><mi>a</mi><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac></msup><mo>*</mo><msup><mi>b</mi><mfrac><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mn>2</mn></mfrac></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>coef1</mi><mo>+</mo><mi>coef2</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>2</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>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pregunta</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msqrt><msup><mi>x</mi><mn>3</mn></msup></msqrt><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup></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>12012000000</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><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"></data></localData></question> VA_AI_22 T. Binomio (Coeficientes 2) Calcule el producto de los coeficientes numéricos del primer y del último término del desarrollo ordenado
del binomio:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»#«/mo»«mi»x«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»#«/mo»«mi»x«/mi»«mi»b«/mi»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»n«/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>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>xa</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mi>m</mi><mo>,</mo><msup><mi>m</mi><mn>2</mn></msup><mo>,</mo><msup><mi>m</mi><mn>3</mn></msup><mo>,</mo><msup><mi>m</mi><mn>4</mn></msup><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>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xb</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mn>1</mn><mi>m</mi></mfrac><mo>,</mo><mfrac><mn>1</mn><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo>,</mo><msqrt><mi>m</mi></msqrt><mo>,</mo><msqrt><msup><mi>m</mi><mn>3</mn></msup></msqrt><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>5</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><msup><mi>a</mi><mi>n</mi></msup><mo>*</mo><msup><mi>b</mi><mi>n</mi></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>2562890625</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></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_23 Suma de Combinatorias Calcule la suma de los siguientes coeficientes binomiales:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»+«/mo»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»+«/mo»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/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"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>17</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>k</mi><mo>=</mo><mn>0</mn></mrow><mi>a</mi></munderover><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>a</mi><mi>k</mi></apply></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>12</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>4096</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><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_24 T. Binomio (Sumatoria) Utilice el teorema del Binomio para calcular

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»0«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/munderover»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»k«/mi»«mo»+«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«msup»«mo»)«/mo»«mi»k«/mi»«/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>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>3</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>k</mi><mo>=</mo><mn>0</mn></mrow><mi>a</mi></munderover><mo>(</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>b</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></apply><mo>*</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mi>k</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>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>15</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>2003</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> VA_AI_25 T. Binomio (Existencia de un término) Encuentre, si existe, el coeficiente que acompaña a

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«/math» en el desarrollo de

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#160;«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mn»3«/mn»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/math»

SI NO EXISTE, ESCRIBA UNA p

 

 

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