Answer
The series converges. The sum of the infinite geometric series is $\frac{1}{648}$
Work Step by Step
The series is convergent because |r| $\lt$ 1.
r (the common ratio) = $\frac{1}{9}$ since each term is multiplied by $\frac{1}{9}$.
Use the formula for the sum of an infinite geometric series: S = $\frac{a}{1-r}$ and plug in the first term, $\frac{1}{729}$, for a, and the common ratio, $\frac{1}{9}$ for r: S = $\frac{\frac{1}{729}}{1-\frac{1}{9}} = \frac{\frac{1}{729}}{\frac{8}{9}}$ = $\frac{1}{648}$
