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