Answer
Diverges
Work Step by Step
We have: $a_k=\dfrac{1}{k}+\dfrac{2}{k}$ and $b_k=\dfrac{1}{k}$
Now, we can see that
$\dfrac{1}{k}+\dfrac{2}{k} \gt \dfrac{1}{k}$
But the series $\Sigma_{k=1}^{\infty} \dfrac{1}{k}$ is a harmonic series which is a divergent series .
Therefore, the series diverges by the comparison test.
