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: 57


$\Sigma b_n$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.
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