can some one give me an example of a sequence of numbers vn such that its mean tends to a limit, but vn does not.
I was thinking about an uniform function or something like that, but I am not quite sure.
2026-04-23 15:03:19.1776956599
sequence and its mean converge to different limits
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The sequence $u_n = (-1)^n$ is such an example, since you can check that $$ \lim \frac 1n \sum_{i=1}^n (-1)^n = 0, $$
while $u_n$ does not have a limit. You may want to take a look at "Cesaro sums".