# Terms of a monotone, convergent series must be $o(1/n)$ [duplicate]

Let $(x_n)_{n\in\mathbb N}$ be a non-negative, non-increasing sequence such that $\sum_{n=1}^{\infty} x_n<\infty$. I want to show that $$\lim_{n\to\infty}\{nx_n\}=0.$$ I’ve definitely seen this question asked on this forum before, but I’m unable to find it now. Any reference or hint would be appreciated.