$\"\"$

The series is $\"\"$ .

Consider the series $\"\"$ .

$\"\"$

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

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

$\"\"$

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 less than the converging series is also convergent.

Therefore, $\"\"$ is convergent by part (i) of the Comparison Test.

$\"\"$

$\"\"$ is convergent.