# Calc6.43

Discuss the convergence or divergence of the series $\sum _{{n=1}}^{{\infty }}{\frac {n}{(n+2)!}}$.
$\lim _{{n\rightarrow \infty }}\left|{\frac {{\frac {n+1}{(n+3)!}}}{{\frac {n}{(n+2)!}}}}\right|=\lim _{{n\rightarrow \infty }}\left|{\frac {n+1}{n(n+3)}}\right|=0\,$