Answer
Converges
Work Step by Step
Here, we have the given series $\Sigma_{n=1}^{\infty} \dfrac{3}{n \sqrt n}$
Re-write the given series in the simplest form:
$\Sigma_{n=1}^{\infty} \dfrac{3}{n \sqrt n}=\Sigma_{n=1}^{\infty} \dfrac{1}{n^{3/2}}$
From the above series, we can see that the series shows a p-series with $p=\dfrac{3}{2} \gt 1$.
Hence, we can conclude that the given series converges by p-series test.
