Answer
$S= (\frac{4}{15})$
Work Step by Step
Formula to find the Nth partial sum of a geometric series is :
$S_{n}=\frac{a(1−r^{n})}{1−r}$
Formula to find the sum of a geometric series is :
$S=\frac{a}{1−r}$
Here
a = $(\frac{-2}{3})^{2}$
r = $(\frac{-2}{3})$
Thus,
$S=\frac{a}{1−r}$
$S=\frac{(\frac{-2}{3})^{2}}{1−(\frac{-2}{3})}$
$S=\frac{(\frac{4}{9})}{(\frac{5}{3})}$
$S= (\frac{4}{15})$
