Answer
The Sum of given infinite geometric series = $\frac{3}{2}$
Work Step by Step
The Sum of a infinite geometric series ( if | r | $\lt$ 1 ) is given by
S = $\frac{First term }{1 - common ratio}$ = $\frac{a_{1}}{1 - r}$
The given infinite geometric series
= 1 + $\frac{1}{3}$ + $\frac{1}{9}$ + $\frac{1}{27}$ + ......................
Here
First term $a_{1}$ = 1
common ratio r = $\frac{\frac{1}{27}}{\frac{1}{9}}$ = $\frac{\frac{1}{9}}{\frac{1}{3}}$ = $\frac{\frac{1}{3}}{1}$ = $\frac{1}{3}$
The Sum S = $\frac{a_{1}}{1 - r}$ = $\frac{1}{1 - \frac{1}{3}}$ = $\frac{1}{\frac{2}{3}}$ = $\frac{3}{2}$
