Answer
The series is convergent. The sum of the infinite geometric series is $-\frac{1000}{117}$
Work Step by Step
The series is convergent because |r| $\lt$ 1.
r (the common ratio) = $-\frac{3}{10}$ since each term is multiplied by $-\frac{3}{10}$.
Use the formula for the sum of an infinite geometric series: S = $\frac{a}{1-r}$ and plug in the first term, $-\frac{100}{9}$, for a, and the common ratio, $-\frac{3}{10}$ for r: S = $\frac{-\frac{100}{9}}{1-(-\frac{3}{10})} = \frac{-\frac{100}{9}}{\frac{13}{10}}$ = $-\frac{1000}{117}$
