Determine the radius of convergence of the power series:
Test for convergence at the boundary points if is finite.
If then unless . Thus, the series does not converge for if .
If then we apply Dirichlet’s test where
is bounded for any (i.e., the partial sums are bounded) and the terms are monotonically decreasing with . Hence, the series converges for , which implies if .
If then for all so the series converges for all which implies .