Question

Cual es la solución al problema?

Answer 1

RESPUESTAS


cualquiera de las dos respuesta es valida

$\frac{1}{1024} \: o \: tambien \: \frac{1}{ {2}^{10} }$




EXPLICACIÓN PASO A PASO

$\frac{1}{ {2}^{12} } + \frac{2}{ {2}^{13} } + \frac{4}{ {2}^{14} } + \frac{8}{ {2}^{15} } \\ aplicamos \:leyes \: de exponentes \\ (4 = {2}^{2} ).(8 = {2}^{3} ) \\ {a}^{3} = {a}^{2+ 1} = {a}^{2} \times {a}^{1} \\ \\ aplicando \: \\ \frac{1}{ {2}^{12} } + \frac{2}{ {2}^{13} } + \frac{4}{ {2}^{14} } + \frac{8}{ {2}^{15} } \: \\ \\ \frac{1}{ {2}^{12} } + \frac{2}{ {2}^{12 + 1} } + \frac{ {2}^{2} }{ {2}^{12 + 2} } + \frac{ {2}^{3} }{ {2}^{12 + 3} } \\ \\ \frac{1}{ {2}^{12} } + \frac{2}{ {2}^{12 } \times 2 } + \frac{ {2}^{2} }{ {2}^{12 } \times {2}^{2} } + \frac{ {2}^{3} }{ {2}^{12 } \times {2}^{3} } \\ \\ \frac{1}{ {2}^{12} } + \frac{1}{ {2}^{12 } } + \frac{ 1 }{ {2}^{12} } + \frac{ 1}{ {2}^{12} } \\ \\ sumando \\ \frac{1 + 1 + 1 + 1}{ {2}^{12} } \\ \\ \frac{4}{ {2}^{10 + 2} } = \frac{ {2}^{2} }{ {2}^{10} \times {2}^{2} } = \frac{1}{ {2}^{10} } = \frac{1}{1024} > respuesta <$