Prove that $y_n$ = $\frac{6^n}{n!}$ is contractive Prove that $y_n$ = $\frac{6^n}{n!}$ is contractive.
My attempt at this question is to compare $\frac{|y_{n+2}-y_{n+1}|}{|y_{n+1}-y_{n}|}$. Doing this got me to $\frac{|24-6n|}{|-n^2+3n+10|}$, but I don't know how to get a constant to prove that it is contractive.

$\frac{|24-6n|}{|-n^2+3n+10|}$
= $\frac{6|4-n|}{|-n^2+3n+10|}$
$<=$ $\frac{|4-n|}{|-n^2+3n+10|}$
$=$ $\frac{|n-4|}{|-n^2+3n+10|}$
$<=$ $\frac{|n|}{|-n^2+3n+10|}$
$<=$ $\frac{|n|}{|3n|}$
=  $\frac{1}{3}$
0 < 1/3 < 1 , so we have a contractive sequence
