try the ratio test
so a(n+1)/a(n) = L
and the series is only convergent when L < 1
so if you can come up with an inequality and then solve for z
Find the radius of convergence of the given power series.
I'm not sure how to use the theorems given in my book to solve these.
Theorem: Suppose that is a power series with a positive or infinite radius of convergence R.
(a) If exists, then
(b) If exists, then
Any help would be appreciated, thanks!