Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 11 - Section 11.4 - The Comparison Tests - 11.4 Exercises - Page 731: 2

Answer

a) $\Sigma a_{n}$ is divergent. b) You cannot say anything about $\Sigma a_{n}$

Work Step by Step

a) Given $a_{n} > b_{n}$ for all $n$ and $\Sigma b_{n}$ is divergent, since $a_{n} \geq b_{n}$ is true for all $n$, $\Sigma a_{n}$ is divergent by the Comparison Test. b) To use the Comparison Test, $a_{n} \geq b_{n}$ for all $n$ when $\Sigma b_{n}$ is divergent. If $a_{n} < b_{n}$, we cannot use the comparison test, and therefore, we cannot say anything about $\Sigma a_{n}$.
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.