Answer
Converges
Work Step by Step
We are given that $\Sigma a_n$ is convergent.
and $\Sigma a_n \gt 0$ and $\Sigma b_n \gt 0$
Let us consider $l=\lim\limits_{n \to \infty} \dfrac{(a_n)^2}{a_n} =\lim\limits_{n \to \infty} a_n=0$
Hence, the given series $\Sigma _{n=1}^\infty (a_n)^2$ converges by the limit comparison test.
