The goal is to show that,
$\frac{M}{k^2}<{n \choose k}$,
where, M > 0, n is in (0, 1), and k is a positive integer. I have tried a handful of different strategies to solve this, but I havn't made any progress whatsoever in any of my strategies. I feel like I am missing something. When I plot this, this does hold true though. Is there any relations I am missing that would assist in this?