University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.4 - Comparison Tests - Exercises - Page 509: 58



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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.