Answer
The series is convergent. The sum of the infinite geometric series is $\frac{2}{3}$
Work Step by Step
The series is convergent because |r| $\lt$ 1. r (the common ratio) = $\frac{2}{5}$ since each term is multiplied by $\frac{2}{5}$.
Use the formula for the sum of an infinite geometric series: S = $\frac{a}{1-r}$ and plug in the first term, $\frac{2}{5}$, for a, and the common ratio, $\frac{2}{5}$ for r: S = $\frac{\frac{2}{5}}{1-\frac{2}{5}} = \frac{\frac{2}{5}}{\frac{3}{5}}$ = $\frac{2}{3}$
