Question

Calcular el valor de A= 1/ 3 + 2/ 9 + 1/ 9 + 4/ 81 + 5/ 243 + .......

A. 3/5
B. 4/3
C. 3/4
D. 1/2
E. 5/3

Answer 1

Hola (｡•̀ᴗ-)✧

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Si: |x| > 1

$\boxed{\sum_{n=1}^{\infty} \frac{n}{x^n} = \frac{x}{(x-1)^2} }$

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Calcular el valor de :

$A = \frac{1}{3} + \frac{2}{9} + \frac{1}{9} + \frac{4}{81} + \frac{5}{243 } + ...$

$A = \frac{1}{3} + \frac{2}{9} + \frac{3}{27} + \frac{4}{81} + \frac{5}{243 } + ...$

$A = \frac{1}{3} + \frac{2}{3^2} + \frac{3}{3^3} + \frac{4}{3^4} + \frac{5}{3^5 } + ...$

$A = \frac{3}{ {(3 - 1)}^{2} } = \frac{3}{ {2}^{2} } = \frac{3}{4}$

C) 3/4