$\"\"$

Alternating Series Test :

If the alternating series $\"\"$ satisfies

(i) $\"\"$ ,

(ii) $\"\"$ , then the series is convergent.

$\"\"$

The series is $\"\"$ .

The function $\"\"$ is decreasing function.

The sequence $\"\"$ is eventually decreasing.

Thus, condition (i) is verified.

$\"\"$

Find $\"\"$ .

$\"\"$

$\"\"$ .

Thus the given series is convergent by the Alternating Series Test.

$\"\"$

The series $\"\"$ is convergent.