The series is .

Limit comparision test :

The series is converges if .

Consider .

Therefore, the series is converges by limit comparision test.

But the series diverges.

Alternate series test :

Let ,The alternate series test and converge if it satisfies

the following conditions.

(1). ,

(2). for all values of  .

Here .

.

and .

Hence .

Since the series is converges by alternating series test.

Therefore, the series is converges conditionally.

The series is converges conditionally.