\ \

The series is . \ \

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. \ \

Here and . \ \

\ \

\ \

\ \

. \ \

. \ \

Therefore, the series is converges by using ratio test. \ \

The series is converges by using ratio test.