For f(x), apply the ratio test and find the limit as . Then check the endpoints as well. It converges at x=2.

By the ratio test:

The ratio test gives cionvergence for and divergence for

Solving the first inequality we get .

At x=1, the series is , which is a divergent p-series.

At x=3, it is convergent and converges to -ln(2).

So, the convergence set is

Check it out. Make sure I did not err somewhere, then run a test on the derivatives of the series.