The series is .

.

Consider the series .

Hence .

The general form of -series is .

The series is converges is and only if .

The series is converges where .

Therefore, the series converges.

Alternate series test :

Let ,The alternate series test and converge if it satisfies the following conditions.

(1). ,

(2). for all values of .

.

.

Condition is satisfied.

.

Condition is satisfied.

Therefore, the series is convergence by the Alternating series test.

The series is convergence by the Alternating series test.