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 .

Consider .

Find .

.

Therefore, and either both converges or diverges.

The series is converges if and only if is converges.

The series is in the form of -series.

The -series is , if , then the series is converges.

is converges, if and only if .

The series is converges if and only if .

The series is converges if and only if .