2.10.97 Number series

Condition: Investigate the convergence of a number series using necessary or sufficient characteristics: \[ \sum_{n=1}^{\infty} \frac{n^{2}}{e^{n^{3}}}, \quad \sum_{n=1}^{\infty} \frac{2^{2 n}}{(n+1)(n+2) !} \]