Ratio Test :

(i) If , then the series is  is absolutely convergent.

(ii) If  or , then the series is  is divergent.

(iii) If , then the ratio test is inconclusive.

The series is .

.

.

. \ \

If then .

.

Since , the series  is converges.

Therefore, the series is converges.

The series converges by Ratio test.