Answer
The Sum of the given infinite geometric series = $\frac{2}{3}$
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 - $\frac{1}{2}$ + $\frac{1}{4}$ - $\frac{1}{8}$ + ......................
Here
First term $a_{1}$ = 1
common ratio r = $\frac{-\frac{1}{8}}{\frac{1}{4}}$ = $\frac{\frac{1}{4}}{-\frac{1}{2}}$ = $\frac{-\frac{1}{2}}{1}$ = - $\frac{1}{2}$
The Sum of the given infinite geometric series = $\frac{a_{1}}{1 - r}$ = $\frac{1}{1 - (-\frac{1}{2})}$ = $\frac{1}{1 + \frac{1}{2}}$ = $\frac{1}{\frac{3}{2}}$ = $\frac{2}{3}$