IMC 2016 · Problem 1

Let $(x_1, x_2, \ldots)$ be a sequence of positive real numbers satisfying $\sum\limits_{n=1}^{\infty} \dfrac{x_n}{2n - 1} = 1$. Prove that

$$\sum_{k=1}^{\infty} \sum_{n=1}^{k} \frac{x_n}{k^2} \le 2.$$