$\"\"$

The two non negative series are $\"\"$ and $\"\"$ .

$\"\"$ and $\"\"$ are convergent.

The series $\"\"$ converges then $\"\"$ .

This means that there exists $\"\"$ with property that $\"\"$ for every $\"\"$ .

Consider the series $\"\"$ .

So, $\"\"$ for $\"\"$ and $\"\"$ converges by comparision to the convrgent series $\"\"$ .

$\"\"$

$\"\"$ is converges.