If $\lim_{n \to\infty}a_n=a$ then $\lim_{n\to \infty}\frac{a_1+a_2+...+a_n}{n}=a$

Asked Oct 22 '16 at 13:06

Active Nov 09 '16 at 08:10

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If $\lim_{n \to \infty}a_n=a$ then $\lim_{n\to \infty}\frac{a_1+a_2+...+a_n}{n}=a$ I need to prove this, and was thinking to use some inequality related to the geometric and harmonic, but unfortunately my efforts did not pan out as hoped. Does anyone know how this would be proven?

edited Nov 09 '16 at 08:10

Martin Sleziak

53,687

asked Oct 22 '16 at 13:06

Roger Federer

Cesaro sum $\ddot\smile$ – Simply Beautiful Art Oct 22 '16 at 13:08
6

See here: http://math.stackexchange.com/questions/207910/prove-convergence-of-the-sequence-z-1z-2-cdots-z-n-n-of-cesaro-means – Robert Z Oct 22 '16 at 13:09

If $\lim_{n \to\infty}a_n=a$ then $\lim_{n\to \infty}\frac{a_1+a_2+...+a_n}{n}=a$

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