## Calculus (3rd Edition)

Published by W. H. Freeman

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

#### Answer

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.

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