Question

Find the radius of convergence and interval of convergence 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 when .

Radius of convergence is .

Interval of convergence is .

Solution:

Radius of convergence is .

Interval of convergence is .