Answer
Diverges
Work Step by Step
We have: $a_k=\dfrac{1}{k^{1/k}}$ and $b_k=\dfrac{1}{k}$
We can see that for $k^{-1/k}= \dfrac{1}{k^{1/k}} \gt \dfrac{1}{k}$ on $(0, \infty)$.
But $b_k=\dfrac{1}{k}$ corresponds to a divergent harmonic series.
Therefore, the series diverges by the comparison test.
