Find the radius of convergence for the series $\sum_{k=0}^{\infty}\frac{k!}{k^k}x^k$.
For other similar problems, I could apply the Ratio Test or the Root Test to find the radius of convergence. For this problem, these tests are not seem to be working. The book says I should take reference to the power series of $e^x$ to determine the endpoints but I can't even find the endpoints of the radius of convergence.