Answer
Converges
Work Step by Step
Consider $a_n=\dfrac{2^{n+1}}{n3^{n-1}}$
Now, $l=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n+1}} |=\lim\limits_{n \to \infty}|\dfrac{\dfrac{2^{n+2}}{(n+1)3^{n}}}{\dfrac{2^{n+1}}{n3^{n-1}}}|$
Thus, we have $l=\lim\limits_{n \to \infty}|\dfrac{2n}{3(n+1)}|=\lim\limits_{n \to \infty}|\dfrac{2n}{3n+3}|=\dfrac{2}{3} \lt 1$
Hence, the series Converges absolutely by the ratio test.