I've calculated the radius of convergence for in two different ways and I get two different answers.Find the range of values of values of x for which the series and converge, and find an expression for their sums, carefully justifying your answers.
The first way:
Alternatively, using the ratio test:
This tells me that .
Which one is correct.
The main problem I have now is trying to find the expression for the sums. Can someone show me how to do that?