Given an increasing sequence of non-negative real numbers $\left(a_{n}\right)_{n=1}^{\infty}$, let

$$s_{n}=\frac{1}{n} \sum_{k=1}^{n} a_{k}$$

Prove that if $s_{n} \rightarrow x$ as $n \rightarrow \infty$ for some $x \in \mathbb{R}$ then also $a_{n} \rightarrow x$ as $n \rightarrow \infty$