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I'm going over properties of limits for series and I'm having trouble proving Arithmetic of infinite series. I know what I'm supposed to do but I can't use standard tricks I'm used to like triangle inequality. Do you have any tips for re - adjusting the epsilon-proofs into M-N proofs?

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closed as off-topic by RRL, Cesareo, Leucippus, Lord Shark the Unknown, KReiser Dec 25 '18 at 7:03

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    $\begingroup$ It's all about neighborhoods: a neighborhood of a point $x$ on the line (by def.) always contains an interval $(x-\varepsilon, x+\varepsilon)$. These are then replaced to the neighborhoods of $+\infty$ which always contain a semiline $(M, \infty)$.. $\endgroup$ – Berci Dec 24 '18 at 9:58