I am really stuck with this excercise:(adsbygoogle = window.adsbygoogle || []).push({});

Let [tex]a_n and b_n[/tex] be two sequences, where [tex]b_n = \frac{a_1 + a_2 + ... + a_n}{n}[/tex] and [tex]lim_(n \rightarrow \infinity) a_n = a[/tex] prove that [tex]lim_(n \rightarrow \infinity) b_n = a[/tex].

I tried to use the definition - [tex]\mid b_n - a \mid < \frac{\mid a_1 - a \mid + \mid a_2 -a \mid + ... + \mid a_n - a \mid}{n}[/tex], but i dont know how to proceed. Any ideas?

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# Homework Help: Limit of a sequence proof

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