Answer
Diverges
Work Step by Step
Re-write the given series as $\Sigma_{n=1}^{\infty} \dfrac{1}{\sqrt[4] {n^{3}}}=\Sigma_{n=1}^{\infty} \dfrac{1}{n^{3/4}}$
Here, we can see that the given series shows a p-series with $p=\dfrac{3}{4}$
Next, $p=\dfrac{3}{4} \lt 1$
This implies that the given series diverges by the p-series test.
