Answer
Diverges
Work Step by Step
For this series $\Sigma_{n=1}^\infty \dfrac{3}{\sqrt n}=3\Sigma_{n=1}^\infty \dfrac{1}{\sqrt n} $
or, $=3\Sigma_{n=1}^\infty \dfrac{1}{n^{1/2}} $
Thus, the given series is a p-series with $p=\dfrac{1}{2} \leq 1$
Hence, the given series diverges.
