Question

Find the sum of the series $1,\frac{2}{5},\frac{4}{25},\frac{8}{125},,.....\infty .$

Answer 1

Here,

$a=1,r=\frac{2}{5}$ and $|r|=|\frac{2}{5}|<1$

Therefore,

$S_{\infty }=\frac{a}{1-r}=\frac{1}{1-\frac{2}{5}}=\frac{5}{3}$