2016 IMO Shortlist A8

Determine the largest real number $a$ such that for all $n \geq 1$ and for all real numbers $x_{0}, x_{1}, \ldots, x_{n}$ satisfying $0=x_{0}<x_{1}<x_{2}<\cdots<x_{n}$, we have $$\frac{1}{x_{1}-x_{0}}+\frac{1}{x_{2}-x_{1}}+\cdots+\frac{1}{x_{n}-x_{n-1}} \geq a\left(\frac{2}{x_{1}}+\frac{3}{x_{2}}+\cdots+\frac{n+1}{x_{n}}\right) .$$

确定最大实数 $a$，使得对于所有 $n \geq 1$ 和所有满足 $0=x_{0}<x_{1}<x_{2}<\cdots<x_{n}$ 的实数 $x_{0}, x_{1}, \ldots, x_{n}$，我们有 $$\frac{1}{x_{1}-x_{0}}+\frac{1}{x_{2}-x_{1}}+\cdots+\frac{1}{x_{n}-x_{n-1}} \geq a\left(\frac{2}{x_{1}}+\frac{3}{x_{2}}+\cdots+\frac{n+1}{x_{n}}\right) 。$$