If (1/x)+(1/2 x2)+(1/4 x3)+(1/8 x4)+(1/16 x5)+ ldots ldots . . ∞=(1/64), then the value of x is

Question

If (1/x)+(1/2 x2)+(1/4 x3)+(1/8 x4)+(1/16 x5)+ ldots ldots . . ∞=(1/64), then the value of x is (A) (125/2) (B) (127/2) (C) (129/2) (D) (131/2)

Tardigrade Admin · Accepted Answer

((1/x)/1-(1)2 x)=(1/64) ⇒ ((1/x)/(2 x-1)2 x)=(1/64) (2/2 x-1)=(1/64) ⇒ 128=2 x-1 ⇒ x=(129/2)

Q. If $\frac{1}{x} + \frac{1}{2 x ^{2}} + \frac{1}{4 x ^{3}} + \frac{1}{8 x ^{4}} + \frac{1}{16 x ^{5}} + \dots\dots ..\infty = \frac{1}{64}$ , then the value of $x$ is