Prove Lim n →∞ n ^ n / (n!) ^ 2 = 0 by using necessary conditions of series convergence

Prove Lim n →∞ n ^ n / (n!) ^ 2 = 0 by using necessary conditions of series convergence

Consider the series N ^ n / (n!) ^ 2
The latter is better than the former = [(n + 1) ^ (n + 1) / (n + 1)! ^ 2] / [n ^ n / (n!) ^ 2]
=[(1 + 1 / N) ^ n] / (1 + n) tends to 0