Answer
Converges
Work Step by Step
We have: $a_k=\dfrac{1}{k^{3/2}+1}$ and $b_k=\dfrac{1}{k^{3/2}}$
Now, we will apply comparison test as:
$\dfrac{1}{k^{3/2}+1} \lt \dfrac{1}{k^{3/2}}$
But the series $\Sigma \dfrac{1}{k^{3/2}}$ is a convergent p-series with $p=\dfrac{3}{2}$.
Therefore, the series converges by the comparison test.
