Question

O numero real X que satisfaz a sentença:

$\frac{1}{x} + \frac{2}{ x^{2} } + \frac{4}{ x^{3} } + \frac{8}{ x^{4} } +...= 1$

Answer 1

Ola Renato

PG 

u1 = 1/x
u2 = 2/x²

q = u2/u1 = (2/x²)/(1/x) = (2/x²)*(x/1) = 2/x

soma infinita
Sn = u1/(1 - q)

Sn = (1/x)/(1 - 2/x) 
Sn = (1/x)/(x - 2)/x = 1/(x - 2)

1/(x - 2) = 1

x - 2 = 1

x = 3