Chapter 11 - Infinite Sequences and Series - Review - True-False Quiz - Page 824: 12

TRUE

Work Step by Step

As we know, $|a_{n}|\gt a_{n}$ Thus , $\Sigma|a_{n}|\gt \Sigma a_{n}$ Since, $\Sigma a_{n}$ diverges when $\Sigma a_{n}=\infty$ and $\Sigma|a_{n}|\gt\infty$ Therefore, $|\Sigma a_{n}|$ diverges. Hence, the statement is TRUE.

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.