ÁLGEBRA 1 COMERCIAL/2 SUMATORIA Y PRODUCTORIA
SUMATORIAS Y PROGRESIONES.08. Dado una sumatoria encontrar otra
Sabiendo que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«mi»a«/mi»«mi»t«/mi»«mi»o«/mi»«mi»s«/mi»«/math», encuentra el valor de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»c«/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>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>t</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ls</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>8</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>n</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>datos1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><munderover><mo>∑</mo><mrow><mrow><mo>#</mo><mn>2</mn></mrow><mo>=</mo><mrow><mo>#</mo><mn>3</mn></mrow></mrow><mrow><mo>#</mo><mn>1</mn></mrow></munderover><mo> </mo><msub><mi>x</mi><mrow><mo>#</mo><mn>2</mn></mrow></msub><mo>=</mo><mo>#</mo><mn>4</mn><mo>"</mo><mo>,</mo><mi>n</mi><mo>,</mo><mi>n1</mi><mo>,</mo><mo> </mo><mn>1</mn><mo>,</mo><mi>suc</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>li</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>p1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</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>p2</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>suc1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><mfrac><mrow><msub><mi>x</mi><mrow><mo>#</mo><mn>1</mn></mrow></msub><mo>+</mo><mo>#</mo><mn>2</mn></mrow><mrow><mo>#</mo><mn>3</mn></mrow></mfrac><mo>"</mo><mo>,</mo><mi>n1</mi><mo>,</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sum1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><munderover><mo>∑</mo><mrow><mrow><mo>#</mo><mn>2</mn></mrow><mo>=</mo><mrow><mo>#</mo><mn>3</mn></mrow></mrow><mrow><mo>#</mo><mn>1</mn></mrow></munderover><mo> </mo><mo>#</mo><mn>4</mn><mo>"</mo><mo>,</mo><mi>ls</mi><mo>,</mo><mi>n1</mi><mo>,</mo><mn>1</mn><mo>,</mo><mi>suc1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inc1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><msub><mi>x</mi><mrow><mo>#</mo><mn>1</mn></mrow></msub><mo>"</mo><mo>,</mo><mi>li</mi><mo>)</mo><mo>,</mo><mi>sum1</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suc3</mi><mo>=</mo><mi>p3</mi><mo>*</mo><msup><mi>n1</mi><mn>2</mn></msup><mo>+</mo><mi>p4</mi><mo>*</mo><mi>n1</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>res1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mn>50</mn><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</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>p4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</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>p5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>ls</mi><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>datos2</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><munderover><mo>∑</mo><mrow><mrow><mo>#</mo><mn>2</mn></mrow><mo>=</mo><mrow><mo>#</mo><mn>3</mn></mrow></mrow><mrow><mo>#</mo><mn>1</mn></mrow></munderover><mo> </mo><mo>(</mo><mo>#</mo><mn>4</mn><mo>)</mo><mo>=</mo><mo>#</mo><mn>5</mn><mo>"</mo><mo>,</mo><mi>ls</mi><mo>,</mo><mi>n1</mi><mo>,</mo><mi>p5</mi><mo>,</mo><mi>suc3</mi><mo>,</mo><mi>res1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inc2</mi><mo>=</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>res2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n1</mi><mo>=</mo><mn>1</mn></mrow><mi>ls</mi></munderover><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>n1</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"><mi>res3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n1</mi><mo>=</mo><mn>1</mn></mrow><mi>ls</mi></munderover><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>n1</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>datos3</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><munderover><mo>∑</mo><mrow><mrow><mo>#</mo><mn>1</mn></mrow><mo>=</mo><mrow><mo>#</mo><mn>2</mn></mrow></mrow><mrow><mo>#</mo><mn>3</mn></mrow></munderover><mo> </mo><mo>(</mo><msub><mi>x</mi><mrow><mo>#</mo><mn>1</mn></mrow></msub><msup><mo>)</mo><mn>2</mn></msup><mo>=</mo><mo>#</mo><mn>4</mn><mo> </mo><mo> </mo><mi>y</mi><mo> </mo><mo> </mo><mo> </mo><munderover><mo>∑</mo><mrow><mrow><mo>#</mo><mn>1</mn></mrow><mo>=</mo><mrow><mo>#</mo><mn>2</mn></mrow></mrow><mrow><mo>#</mo><mn>3</mn></mrow></munderover><mo> </mo><msub><mi>x</mi><mrow><mo>#</mo><mn>1</mn></mrow></msub><mo>=</mo><mo>#</mo><mn>5</mn><mo>"</mo><mo>,</mo><mi>n1</mi><mo>,</mo><mn>1</mn><mo>,</mo><mi>ls</mi><mo>,</mo><mi>res3</mi><mo>,</mo><mi>res2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p6</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>p7</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"><mi>inc3</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><munderover><mo>∑</mo><mrow><mrow><mo>#</mo><mn>1</mn></mrow><mo>=</mo><mrow><mo>#</mo><mn>2</mn></mrow></mrow><mrow><mo>#</mo><mn>3</mn></mrow></munderover><mo>(</mo><mo>#</mo><mn>4</mn><mo>*</mo><msub><mi>x</mi><mrow><mo>#</mo><mn>1</mn></mrow></msub><mo>+</mo><mo>#</mo><mn>5</mn><msup><mo>)</mo><mn>2</mn></msup><mo>"</mo><mo>,</mo><mi>n1</mi><mo>,</mo><mn>1</mn><mo>,</mo><mi>ls</mi><mo>,</mo><mi>p6</mi><mo>,</mo><mi>p7</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>datos</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>datos1</mi><mo>,</mo><mi>datos2</mi><mo>,</mo><mi>datos3</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">if</csymbol><mrow><mi>datos</mi><mo>=</mo><mi>datos1</mi></mrow><mrow><mi>inc</mi><mo>=</mo><mi>inc1</mi></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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>datos</mi><mo>=</mo><mi>datos2</mi></mrow><mrow><mi>inc</mi><mo>=</mo><mi>inc2</mi></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">if</csymbol><mrow><mi>datos</mi><mo>=</mo><mi>datos3</mi></mrow><mrow><mi>inc</mi><mo>=</mo><mi>inc3</mi></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">if</csymbol><mrow><mi>inc1</mi><mo>=</mo><mi>sum1</mi></mrow><mrow><mi>sol1</mi><mo>=</mo><mfrac><mn>1</mn><mi>p2</mi></mfrac><mo>*</mo><mi>evaluar</mi><mo>(</mo><mi>suc</mi><mo>,</mo><mi>ls</mi><mo>)</mo><mo>+</mo><mfrac><mi>p1</mi><mi>p2</mi></mfrac><mo>*</mo><munderover><mo>∑</mo><mrow><mi>n1</mi><mo>=</mo><mn>1</mn></mrow><mi>ls</mi></munderover><mn>1</mn></mrow><mrow><mi>sol1</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><mi>suc</mi><mo>,</mo><mi>li</mi><mo>)</mo><mo>-</mo><mi>evaluar</mi><mo>(</mo><mi>suc</mi><mo>,</mo><mi>li</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mrow><mi>res1</mi><mo>-</mo><munderover><mo>∑</mo><mrow><mi>n1</mi><mo>=</mo><mi>p5</mi></mrow><mi>ls</mi></munderover><mo>(</mo><mi>p3</mi><mo>*</mo><msup><mi>n1</mi><mn>2</mn></msup><mo>+</mo><mi>p4</mi><mo>*</mo><mi>n1</mi><mo>)</mo></mrow><mrow><munderover><mo>∑</mo><mrow><mi>n1</mi><mo>=</mo><mi>p5</mi></mrow><mi>ls</mi></munderover><mn>1</mn></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><msup><mi>p6</mi><mn>2</mn></msup><mo>*</mo><mi>res3</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>p6</mi><mo>*</mo><mi>p7</mi><mo>*</mo><mi>res2</mi><mo>+</mo><msup><mi>p7</mi><mn>2</mn></msup><mo>*</mo><munderover><mo>∑</mo><mrow><mi>n1</mi><mo>=</mo><mn>1</mn></mrow><mi>ls</mi></munderover><mn>1</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>datos</mi><mo>=</mo><mi>datos1</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>sol1</mi></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">if</csymbol><mrow><mi>datos</mi><mo>=</mo><mi>datos2</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>sol2</mi></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">if</csymbol><mrow><mi>datos</mi><mo>=</mo><mi>datos3</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>sol3</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>datos3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∑</mo><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow><mn>6</mn></munderover><mo> </mo><msub><ms>(x</ms><mi>t</mi></msub><msup><ms>)</ms><mn>2</mn></msup><mo>=</mo><mn>1790</mn><mo> </mo><mo> </mo><ms>y</ms><mo> </mo><mo> </mo><mo> </mo><munderover><mo>∑</mo><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow><mn>6</mn></munderover><mo> </mo><msub><ms>x</ms><mi>t</mi></msub><mo>=</mo><mn>52</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>datos2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∑</mo><mrow><mi>t</mi><mo>=</mo><mn>3</mn></mrow><mn>6</mn></munderover><mo> </mo><ms>(</ms><mi>c</mi><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>t</mi><ms>)</ms><mo>=</mo><mn>370</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>datos1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∑</mo><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mo> </mo><msub><ms>x</ms><mi>t</mi></msub><mo>=</mo><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inc3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∑</mo><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow><mn>6</mn></munderover><ms>(</ms><mn>3</mn><mo>*</mo><msub><ms>x</ms><mi>t</mi></msub><mo>+</mo><mn>1</mn><msup><ms>)</ms><mn>2</mn></msup></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>16428</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"><mfrac><mn>135</mn><mn>2</mn></mfrac></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>8</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>16428</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^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>