## University Calculus: Early Transcendentals (3rd Edition)

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.