#### Answer

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.