Sunday, 23 March 2014

factorial - How find the limit of limlimitsntoinftyleft(n1right)!

I have the next limit: lim



I had done some steps and simplified it to:
\lim\limits_{n\to \infty }\left(1-\frac{2}{n!+1}\right)^{(n+1)(n-1)!}=\\ \lim\limits_{n\to \infty }\left(1-\frac{1}{(n(n-1)!+1)\cdot 0.5}\right)^{(n+1)(n-1)!}




And my final result is:



\lim\limits_{n\to \infty }\left(\frac{1}{e}\right)^{\frac{3n+2+\frac{1}{(n-1)!}}{2}}



My question is what happens to \frac{1}{(\infty -1)!}? Is it 0?

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