Non existence of a limit with sum – math.stackexchange.com

Non existence of a limit with sum – math.stackexchange.com

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Find a $$ $n\in\Bbb N$ and $0\le b_n\le 1$ such as the limit $$\lim_{n\to\infty} {\frac1n}\sum_{i=1}^{n-1}b_i$$ does not exist. I don't know how to deal with this problem, it seems to me that ...

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