Answer
Converges
Work Step by Step
Here, we have the given series as $\Sigma_{n=1}^{\infty} \dfrac{1}{ n^{5/2}}$
Here, we can see that the given series shows a p-series with $p=\dfrac{5}{2}$
Next, $p=\dfrac{5}{2} \gt 1$
This implies that the given series converges by the p-series test.
