Answer
Convergent
Work Step by Step
Given: $\Sigma a_n$ is convergent.
Also, $\Sigma a_n \gt 0$ and $\Sigma b_n \gt 0$
This implies that $\lim\limits_{n \to \infty} \dfrac{a_n}{b_n} =\infty$
Thus, we can see that the series $\Sigma b_n$ is a convergent series by the limit comparison test.
Therefore, the series $\Sigma b_n$ is convergent.
