Answer
Converges
Work Step by Step
Let $u_n=\dfrac{1}{n3^{n}}$
When the numerator increases, the value of fraction is always increasing and also, when the denominator decreases, the value of fraction is always increasing.
$\implies a_n \leq \dfrac{1}{3^{n}}$
we can see that the series $\Sigma_{n=1}^\infty \dfrac{1}{3^n}$ shows a convergent geometric series and has common ratio $r=\dfrac{1}{3} \gt 1$ .
Hence, the series converges by the comparison test.