Answer
$\dfrac{3}{2}$
Work Step by Step
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
Since, we have $\sum_{n =0}^{ \infty} (\dfrac{2}{3})^n$ and $\sum_{n =0}^{ \infty} (\dfrac{1}{3})^n$
We have a convergent geometric series with first term, $a=1$ and common ratio $r =\dfrac{2}{3}, \dfrac{1}{3}$
We find the difference between the sums of the two geometric series thus:
Thus, $S=\dfrac{1}{1-\dfrac{2}{3}}-\dfrac{1}{1-\dfrac{1}{3}}=\dfrac{3}{3-1}=\dfrac{3}{2}$
