I have come across this in a proof:
If $t>2n^2$ then, $t!>(n^2)^{t-n^2}=n^tn^{t-2n^2}>n^t$ Obviously, this is much help to determine the relationship between factorials and exponential, but I fail to see the motivation behind the initial assumption.
Is there a different way to think about this or derive the same result?