Task is to show that
There exists some $n_{0} \in \mathbb N $, $\forall n \in \mathbb N $
$ (n_{0} \ge n \Rightarrow n! - n^4 \ge n^2 - 11n)$
Where to start with this?
By Induction over $n$, assuming $n_{0} =1:$
Holds for $n_{0} =1:$
Assume $ k! - k^4 \ge k^2 - 11k $
Show: $ (k+1)! - (k+1)^4 = ....$
Do not want the answer just headsup on the approach.. Thanks.