Answer
Diverges
Work Step by Step
Consider $a_n=\dfrac{2n}{3n-1}$
Now, $\lim\limits_{n \to \infty} a_n =\lim\limits_{n \to \infty}\dfrac{2n}{3n-1}$
Thus, we have $=\dfrac{2}{3}$
and $\dfrac{2}{3} \ne 0$
Hence, the series diverges due to the n-th term test.