Proving of an inequality of a sequence – math.stackexchange.com

Proving of an inequality of a sequence – math.stackexchange.com

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The question I am stuck on is that there is a sequence $(x_n)$ with $$\forall n \in \mathbb{N}: |x_{n+1} - x_n| \leq \frac{1}{n(n+1)} $$ It asks to prove that $$\forall m \in \mathbb{N}:\forall n ...

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