radius of convergence and interval of convergence of the series

I used the ratio test and after some cancellations, i get



not sure if what i got so far is correct but i get stuck after i get to this part.

How do i finish this problem? thanks!

After applying the ratio test, you should get

instead of another sigma.

To find the radius of convergence, you simply have to find the values of x that would make the series converge.

ahh silly mistake from me. forgot about that. thanks!