Question

SERIES Y SUMATORIAS.- Hallar el valor de ''E'':

Answer 1

Respuesta:

Alternativa C) 13/220

Explicación paso a paso:

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$\frac{a}{n \times (n + b)} = \frac{a}{b} \times (\frac{1}{n} - \frac{1}{n + b} )$

$e =\frac{1}{3} \times( \frac{1}{5} - \frac{1}{8}) + \frac{1}{3} \times ( \frac{1}{8} - \frac{1}{11} ) + \frac{1}{3} \times ( \frac{1}{11} - \frac{1}{14} ) + ... + \frac{1}{3} \times ( \frac{1}{41} - \frac{1}{44} ) \\ e = \frac{1}{3} \times( \frac{1}{5} - \frac{1}{8}+ \frac{1}{8} - \frac{1}{11} + \frac{1}{11} - \frac{1}{14} + ... \frac{1}{41} - \frac{1}{44} ) \\ e = \frac{1}{3} \times( \frac{1}{5} - \frac{1}{44} ) \\ e = \frac{1}{3} \times \frac{(44 - 5)}{44 \times 5} \\ e = \frac{39}{3 \times 44 \times 5} \\ e = \frac{13}{44 \times 5} \\ e = \frac{13}{220}$