$\"\"$

The series is $\"\"$ .

Consider the series $\"\"$ .

$\"\"$ .

It is geometric series with common ratio $\"\"$ .

Geometric series with $\"\"$ , is divergent.

$\"\"$

Compare the series $\"\"$ with $\"\"$ .

The Comparison Test:

Suppose that $\"\"$ and $\"\"$ are series with positive terms.

(i) If $\"\"$ is convergent and $\"\"$ for all $\"\"$ , then $\"\"$ is also convergent.

(ii) If $\"\"$ is divergent and $\"\"$ for all $\"\"$ , then $\"\"$ is also divergent.

Here $\"\"$ .

Thus, by the comparision test series greater than the diverging series is also divergent.

Therefore $\"\"$ is divergent by part (ii) of the comparison Test.

$\"\"$

$\"\"$ is divergent.