Answer
Converges
Work Step by Step
Let us consider $a_n=\dfrac{(-2)^n}{3^n}$
Apply direct comparison test.
This implies that $\Sigma_{n=1}^\infty \dfrac{(-2)^n}{3^n} \leq \Sigma_{n=1}^\infty \dfrac{(2)^n}{(3)^n}=\Sigma_{n=1}^\infty (\dfrac{2}{3})^{n} $
Here, the series $\Sigma_{n=1}^\infty (\dfrac{2}{3})^{n}$ shows a geometric convergent series.
Thus, the series converges by the direct comparison test.