KöMaL 2017 A709

Let $a>0$ be a real number. Find the minimal constant $C_a$ for which the inequality $C_a\sum_{k=1}^n \frac1{x_k-x_{k-1}} >\sum_{k=1}^n \frac{k+a}{x_k}$ holds for any positive integer $n$ and any sequence $0=x_0<x_1<\cdots<x_n$ of real numbers.