Question

Find the sum to infinity of the geometric series $2+\frac{2}{3}+\frac{2}{9}+$ ..........

Answer 1

Here, $a=2,r=\frac{\frac{2}{3}}{2}=\frac{2}{3}\times \frac{1}{2}=\frac{1}{3},S_{\infty }=?$

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