Question

Determine the convergence or divergence of the series.

Answer 1

Step 1:

The series is .

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.

Here  and .

Find . 

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

Solution:

The series is convergent.