How to show that for any real numbers $\{a_n\}$ if $a_n\to 0$, then $\frac{a_1+\dots+a_n} {n}\to 0$.
I am a beginner to learn real analysis. Can any one give some suggestion?
Thank you!
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1Eventually they will all be less than $\epsilon$. – Michael Dec 16 '19 at 05:03
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2Does this answer your question? On Cesàro convergence: If $ x_n \to x $ then $ z_n = \frac{x_1 + \dots +x_n}{n} \to x $ – csch2 Dec 16 '19 at 06:01