## Thomas' Calculus 13th Edition

Formula to calculate the sum of a geometric series is: $S=\dfrac{a}{1-r}$; Consider the series $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \dfrac{n!}{n^n}$ . As we can see that the terms for numerator will be increasing much than the terms on denominator. Also, $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \dfrac{n!}{n^n}=\infty \ne 0$ Hence, the given diverges.