Determine the radius of convergence of the power series:
Test for convergence at the boundary points if is finite.
This is an alternating series, and we have
If then the terms are not going to 0 so the series is divergent. If then it is monotonically decreasing, so we know (by the Leibniz rule) that the series converges if and only if
Therefore, the radius of convergence is , and the series converges at every boundary point .