Series Convergence Divergence

Question

Answer 1

Step 1:

The series is

Rewrite the series in summation form

Ratio test :

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

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

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

Step 2:

Here  and .

Find . 

If , then .

Hence, by the ratio test, the series is convergent.

Solution:

The series is convergent.