If $\sum a_n$ is a convergent series with $S = \lim s_n$, where $s_n$ is the nth partial sum, then $\lim_{n \to \infty} \frac{s_1+...+s_n}{n} = S$
Prove convergence of the sequence $(z_1+z_2+\cdots + z_n)/n$ of Cesaro means