# Comparing $\left[(\frac{u+1}{2n})^{2n} - (\frac{u}{2n})^{2n}\right]$ to $\left[(u+1)^n-u^n\right]$

Given $(u+1) \le n^2$, I am trying to understand under what circumstances:

$\left[(\frac{u+1}{2n})^{2n} - (\frac{u}{2n})^{2n}\right]$ < $\left[(u+1)^n-u^n\right]$

It seems like it should be easy to prove but I'm not sure where to begin.

At this point, I am thinking that the approach requires using the Binomial Theorem? Is that right? Or is it enough to figure out the first derivative?

A sufficient condition is when $u,n \ge 0$.