Answer
Converges absolutely.
Work Step by Step
The series will converge conditionally when it is a convergent series , but the condition is when the series of its absolute value diverges and the series will converge absolutely but the condition is when the series of its absolute value converges.
The convergence of a p-series can be stated as when an infinite series let us say $\sum_{n=1}^{n=\infty} \dfrac{1}{n^p}$ converges when $p \gt 1$ and
and otherwise it will diverge.
Here, in the problem we have $\sum_{k=1}^{\infty} \dfrac{1}{k^{3/2}}$, where $p=\dfrac{3}{2} \gt 1$. This implies that the given series converges by p-test.
Thus, we can conclude that absolute value of series converges , so the given series converges absolutely.
