If $\lim_{n \rightarrow \infty }s_n = s$, is it true that $\lim_{n \rightarrow \infty} \frac{1}{n}\sum_{k=1}^n s_k =s $ as well?
On Cesàro convergence: If $ x_n \to x $ then $ z_n = \frac{x_1 + \dots +x_n}{n} \to x $