So I had to calculate the radius of convergence of

around the point

This is how I tried it. I'd love to hear what is wrong with my attempt:http://www.sb.hik.se/personal/sanno/.../Chapter_5.pdf

V.4.1.f) The Answer is 2.

First I rewrote it

Then with partial fractioning:

So we can write are original function as :

And use the geometric series formula:

And finally apply the ratio test to the coefficients:

So I guess R would be one.

Please, not only advise me how to find the radius of convergence. Please tell me if I made any mistakes above (particularly in method.)