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