Answer
Converges
Work Step by Step
We have: $a_k=\dfrac{1}{\sqrt {k^3-k+1}}$ and $b_k=\dfrac{1}{\sqrt {k^3}}$
Now, we can see that
$\dfrac{1}{\sqrt {k^3-k+1}}\leq \dfrac{1}{\sqrt {k^3}}$ for $k \geq 0$
But the series $\Sigma_{k=1}^{\infty} \dfrac{1}{\sqrt {k^3}}=\Sigma_{k=1}^{\infty} \dfrac{1}{k^{3/2}}$ is a p-series series which is a convergent series .
Therefore, the series converges by the direct comparison test.
