Álgebra
***VA-AI-1 Induccion No terminada
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»D«/mi»«mi»e«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»m«/mi»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»u«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»u«/mi»«mi»a«/mi»«mi»l«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»l«/mi»«mi»a«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mi»g«/mi»«mi»u«/mi»«mi»i«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»r«/mi»«mi»o«/mi»«mi»p«/mi»«mi»o«/mi»«mi»s«/mi»«mi»i«/mi»«mi»c«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»o«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»v«/mi»«mi»e«/mi»«mi»r«/mi»«mi»d«/mi»«mi»a«/mi»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»a«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»a«/mi»«mi»r«/mi»«mi»a«/mi»«mspace linebreak=¨newline¨/»«mi»t«/mi»«mi»o«/mi»«mi»d«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«mo»:«/mo»«/math»]]>
1.0000000
0.3333333
0
false
true
abc
Respuesta correcta]]>
Respuesta parcialmente correcta.]]>
Respuesta incorrecta.]]>
#a]]>
#b]]>
#c]]>
<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><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>*</mo><mn>3</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>4</mn><mo>+</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>7</mn><mo>)</mo></mrow><mn>6</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mi>n</mi></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><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>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>*</mo><mn>3</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>4</mn><mo>+</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>7</mn><mo>)</mo></mrow><mn>6</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mi>n</mi></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><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><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>*</mo><mn>3</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>4</mn><mo>+</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>7</mn><mo>)</mo></mrow><mn>6</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mi>n</mi></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><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>a</mi><mo>=</mo><mo>=</mo><mi>b</mi></mrow><mrow><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>*</mo><mn>3</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>4</mn><mo>+</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>7</mn><mo>)</mo></mrow><mn>6</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mi>n</mi></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><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">if</csymbol><mrow><mi>a</mi><mo>=</mo><mo>=</mo><mi>c</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>a</mi><mo>=</mo><mo>=</mo><mi>c</mi></mrow><mrow><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>*</mo><mn>3</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>4</mn><mo>+</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>7</mn><mo>)</mo></mrow><mn>6</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mi>n</mi></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><mo>}</mo></mrow></apply></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>b</mi><mo>=</mo><mo>=</mo><mi>c</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>b</mi><mo>=</mo><mo>=</mo><mi>c</mi></mrow><mrow><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>*</mo><mn>3</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>4</mn><mo>+</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>7</mn><mo>)</mo></mrow><mn>6</mn></mfrac><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mn>2</mn><mi>n</mi></msup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn><mo>"</mo><mo>,</mo><mo>"</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>5</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>"</mo><mo>}</mo></mrow></apply></apply></math></input></command></group></library><group><command><input><math 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