2.10.97 Number Series

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