CONVERGE O DIVERGE ESTA SERIE ∑_(n=1)^∞▒〖n! lnn/n(n+2)!〗y cual criterio se utiliza

[molly2815]

CONVERGE O DIVERGE ESTA SERIE ∑_(n=1)^∞▒〖n! lnn/n(n+2)!〗y cual criterio se utiliza

∑_(n=1)^∞▒〖n! lnn/n(n+2)!〗Help me please.

 

[pka]

∑_(n=1)^∞▒〖n! lnn/n(n+2)!〗Help me please.

q

I think that your question is about \(\displaystyle \sum\limits_{n = 1}^\infty {\dfrac{{n! \cdot \ln (n)}}{{n\left( {n + 2} \right)!}}} \).

If so, take note that \(\displaystyle ln(n)\le n\) so \(\displaystyle \dfrac{{n! \cdot \ln (n)}}{{n\left( {n + 2} \right)!}} \le \dfrac{1}{{(n + 2)(n + 1)}}\)