The series is .

Limit comparison Test :

Suppose that and  are series with positive terms.

If , where is a finite number and , then either both series converges or both series diverges.

The dominant part of the numerator is  and the dominant part of the denominator is .

Compare the given series with the series .

.

.

Therefore, and either both converges or diverges.

The obtained series is .

.

The series is a geometric series with .

If , then the series is converges.

series is converges.

Therefore, the series is converges.

is convergent.