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