Answer
Converges by Alternating Series Test
Work Step by Step
Rewrite Summation, $\Sigma^{\infty}_{n=1} (-1)^n \frac{1}{3^n}$
Test for two conditions of Alternating Series
i.) $\lim\limits_{n \to \infty} \frac{1}{3^n} =0$
ii.) $a_{n+1} = \frac{1}{3^{n+1}} \leq \frac{1}{3^n} = a_n$
Both condition are satisfied so the Series converges by the Alternating Series Test
