Calculus: Early Transcendentals 8th Edition

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 $\Sigma|a_{n}|\gt\infty$ $|\Sigma a_{n}|$ diverges. Hence, the statement is TRUE.