Answer
The series is convergent. The sum of the infinite geometric series is $\frac{3}{4}$
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 = $\frac{1}{1-(-\frac{1}{3})} = \frac{1}{\frac{4}{3}}$ = $\frac{3}{4}$