Find the radius of convergence for the series ∑n=1∞n!nnxn\sum_{n=1}^{\infty} \frac{n!}{n^n} x^n∑n=1∞nnn!xn using the ratio test.
R=eR = eR=e
R=1eR = \frac{1}{e}R=e1
R=1R = 1R=1
R=∞R = \inftyR=∞