Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - Chapter Review Exercises - Page 591: 13


So, $b_m$ diverges.

Work Step by Step

We have $$ \lim _{m \rightarrow \infty} b_m=\lim _{m \rightarrow \infty} 1+(-1)^m. $$ It is clear that if $m$ is even then $\lim _{m \rightarrow \infty} b_m=2$ and if if $m$ is odd then $\lim _{m \rightarrow \infty} b_m=0$. Hence, the limit does not exist. So, $b_m$ diverges.
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.