Please see the attached worked problem.

Root Test example.pdf

My question is about the final limit:

$\displaystyle \lim_{n\rightarrow\infty} [\frac{n}{n} \cdot \frac{(n-1)}{n} \cdot (n-2)!] $

Can someone show me the steps to get to this point? I am confused as to how the limit becomes this. I know that it is because of the factorial, but it this from canceling due to a telescoping series?

Thanks!