回复 2#郝酒
转发一下AoPS上网友的思路:
Because the following is true.
Let $x_i>0$ such that $\sum\limits_{i=1}^nx_i=n$.
Prove that:
$$\sum_{i=1}^n\frac{\left(2(n-1)x_i\right)^{n-1}}{\left((n-2)x_i+n\right)^{n-1}}\geq n.$$ https://artofproblemsolving.com/community/c6t243f6h1709766