Answer
Convergent
Work Step by Step
Given: $\Sigma a_n$ is convergent.
Also, $\Sigma a_n \gt 0$ and $\Sigma b_n \gt 0$
Now, $\lim\limits_{n \to \infty} \dfrac{(a_n)^2}{a_n} =\lim\limits_{n \to \infty} a_n=0$
Therefore, the series $\Sigma _{n=1}^\infty (a_n)^2$ is convergent by limit comparison test.
