2.10.89 Number series

Condition: Examine the indicated series with positive terms for convergence. 1) \( \sum_{n=1}^{\infty} \frac{n^{n}}{(n+1) !} \) 2) \( \sum_{n=1}^{\infty}\left(\frac{1}{\ln (n+1)}\right)^{2 n}\).