Question

Let $S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....$ find the sum of infinite terms of the series.

Answer 1

Given series is :

$S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.....$

$s_{\infty }=\frac{1}{1-\frac{1}{r}}$
$S_{\infty }=\frac{1}{1-\frac{1}{2}}=2$