Answer
$\Sigma b_n$is a convergent series
Work Step by Step
We are given that $\Sigma a_n$ is convergent.
and $\Sigma a_n \gt 0$ and $\Sigma b_n \gt 0$
Since, we have $\lim\limits_{x \to \infty} \dfrac{a_n}{b_n} =\infty$
Thus, the series $\Sigma b_n$ must also be a convergent series by the limit comparison test.
Hence, the given series $\Sigma b_n$is convergent.
