Chapter 11 - Infinite Sequences and Series - Review - Concept Check - Page 824: 6

(a) A series $\Sigma{a_n}$ is an absolutely convergent if $\Sigma|{a_n}|$ converges. Here, $\Sigma|{a_n}|$ means the sum of the absolute value of the terms. (b) Such series converges since if $\Sigma|{a_n}|$ converges, then $\Sigma|{a_n}|$ also converges. (c) A series $\Sigma{a_n}$ is a conditionally convergent series if $\Sigma|{a_n}|$ diverges but itself converges. Here, $\Sigma|{a_n}|$ means the sum of the absolute value of the terms.

(a) A series $\Sigma{a_n}$ is an absolutely convergent if $\Sigma|{a_n}|$ converges. Here, $\Sigma|{a_n}|$ means the sum of the absolute value of the terms. (b) Such series converges since if $\Sigma|{a_n}|$ converges, then $\Sigma|{a_n}|$ also converges. (c) A series $\Sigma{a_n}$ is a conditionally convergent series if $\Sigma|{a_n}|$ diverges but itself converges. Here, $\Sigma|{a_n}|$ means the sum of the absolute value of the terms.