Determine the radius of convergence of the power series:

Test for convergence at the boundary points if is finite.

Let . Then

This implies the series converges for which implies . Furthermore, the series converges on the boundary except the point . Hence, the series converges for all such that and .

I think there is a typo in the conclusion: the series converges for all $z$ such that $|z+3| \leq 2$, not 3