Question

Qual o valor de: 1/2-1/4+1/8-1/16+....

a)1
b)1/2
c)1/3
d)-1/2
e)2/3

Answer 1

Olá!

$\sum_{n = 1}^{\infty} \frac{(-1)^{n + 1} }{2^n} = \frac{1}{2} - \frac{1}{4} + \frac{1}{8} - \frac{1}{16} + \cdots \\ = \frac{ \frac{1}{2} }{1 -(-\frac{1}{2})} \\ \\ = \frac{ \frac{1}{2} }{1 +\frac{1}{2}} \\ \\ = \frac{ \frac{1}{2} }{ \frac{2 + 1}{2}} \\ \\ = \frac{ \frac{1}{2} }{ \frac{3}{2}} \\ \\ = \frac{1}{ \cancel{2} } \cdot \frac{ \cancel{2} }{3} \\ \\ = \frac{1}{3}$

$\textbf{Alternativa Correcta: C}$

$\textbf{Bons estudos.}$