I'm wondering in how to start this problem. Thank you
2026-04-06 01:09:21.1775437761
Prove that a Cauchy sequence is periodic if and only if it is constant?
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If $a_n$ is periodic of period $M$ and not constant, then there exists $m\in\mathbb{N}$ and $\delta >0$ such that $|a_{(nM)+m}-a_{(nM)}|>\delta$ for any $n\in\mathbb{N}$.