Question

Find the sum of the series $4+2+1+\frac{1}{2}+\frac{1}{4}+.......$ to infinite terms.

Answer 1

Given terms,

$4+2+1+\frac{1}{2}+\frac{1}{4}+.....\infty$

We know that,

$S_{\infty }=\frac{a}{1-r}$

$\begin{array}{c}=\frac{4}{1-\frac{1}{2}}\\ =8\end{array}$

Hence,

We get $8$.