Apply the Root Test to ∑n=1∞nnen⋅n!\sum_{n=1}^{\infty} \frac{n^n}{e^n \cdot n!}∑n=1∞en⋅n!nn. Compute limn→∞ann\lim_{n \to \infty} \sqrt[n]{a_n}limn→∞nan.
1e\frac{1}{e}e1 (converges)
eee (diverges)
111 (inconclusive)
000 (converges)