Question

Find the sum of an infinite G.P : $1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+.......$

• A. $\frac{3}{5}$
• B. $\frac{3}{2}$
• C. $\frac{49}{27}$
• D. $\frac{8}{5}$

Answer 1

The correct option is B $\frac{3}{2}$

Given series is $1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+......$

$a=1,r=\frac{1}{3}$

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

$S_{\infty }=\frac{1}{1-\frac{1}{3}}$

$S_{\infty }=\frac{1}{\frac{2}{3}}$

$\therefore S_{\infty }=\frac{3}{2}$