Limits with factorial I'm having difficulties understanding all limits with factorial... 
Actually, what I don't understand is not the limit concept but how to simplify factorial... 
Example :
$$\lim\limits_{n \to \infty} \frac{(n+1)!((n+1)^2 + 1)}{(n^2+1)(n+2)!}$$
I know that it's supposed to give $0$ as I have the answer, but I'd like to understand how to do it as each time I get a limit with factorial I get stuck.
Thanks.

$\frac{(n+1)!}{(n+2)!} = \frac{1}{n+2}$ 
So, the problem reduces to $lim_{n\rightarrow \infty} \frac{(n+1)^2 + 1)}{(n+2)(n^2 + 1)}$.
The numerator is quadratic in $n$ while the denominator is cubic, so as $n \rightarrow \infty$ the limit should go to $0$. 
