$\"\"$

Statement : If $\"\"$ and $\"\"$ diverges, then the series $\"\"$ diverges.

Direct comparision test :

If $\"\"$ for all $\"\"$ .

1. If $\"\"$ converges, then $\"\"$ converges.

2. If $\"\"$ diverges, then $\"\"$ diverges.

By using the direct comparision test the statement is false.

$\"\"$

The statement is false.