Possible Duplicate:
Two Limits Equal - Proof
Prove convergence of the sequence $(z_1+z_2+\cdots + z_n)/n$ of Cesaro means
Suppose $a_n \rightarrow c$ as $n \rightarrow \infty$. We want to show that $\dfrac{1}{n} \sum_{i=1}^n a_n \rightarrow c$ as $n \rightarrow \infty$.
I know I can use the definition to prove this by showing that for any given $\epsilon$, we can find an $N$ such that whenever $n \ge N$, we can have $|\dfrac{1}{n} \sum_{i=1}^n a_n-c| \le \epsilon$.
I am wondering whether there is another easier way to prove this.
Thank you very much. Hanna