Radius and interval of convergence

Question

Find the radius and interval of convergence of the power series - (sum sign) from n=1 to infinity [(x-3)ⁿ/nIn(n)]. Make sure to identify the test used.

My approach:

1. The center of this series is at x=3
2. The radius is 1
3. Interval of convergence is 2 < x < 4
4. I know we have to use the ratio test

Can someone tell me the steps using the ratio test to find the radius and interval of convergence.

Answer 1

A supplement to Roger's great answer, providing some clearer notation that we unfortunately don't have access to in the text replies.