Answer
$\dfrac{3}{2}$
Work Step by Step
Formula to calculate the sum of a geometric series is:
$S=\dfrac{a}{1-r}$;
Since, we have two series $\sum_{n =0}^{ \infty} (\dfrac{2}{3})^n$ and $\sum_{n =0}^{ \infty} (\dfrac{1}{3})^n$
Both series are a convergent geometric series with first term, $a=1$ and common ratio $r =\dfrac{2}{3}, \dfrac{1}{3}$
Thus, $S=\dfrac{1}{1-\dfrac{2}{3}}-\dfrac{1}{1-\dfrac{1}{3}}$
or, $=\dfrac{3}{3-1}$
or, $=\dfrac{3}{2}$
