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