_ n (1 2 +1 2^2 +1 2^3 + +1 2^n ) equals - Vidyadip

MCQ

$\lim _{n \rightarrow \infty}\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\ldots+\frac{1}{2^n}\right)$ equals

A
2
B
-1
✓
1
D
3

✓

Answer

Correct option: C.

1

(C)
$\lim _{n \rightarrow \infty}\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\ldots+\frac{1}{2^n}\right)=\lim _{n \rightarrow \infty} \frac{1}{2} \frac{\left[1-\left(\frac{1}{2}\right)^n\right]}{\left(1-\frac{1}{2}\right)}$
$=\lim _{n \rightarrow \infty}\left(1-\frac{1}{2^n}\right)$
$=1-0=1$

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