This might sound like a dumb question, but it's actually not too obvious to me. If we know that [itex] \lim_{n→∞}S_{n} = L [/itex], can we prove that [itex] \lim_{n→∞}S_{n-1} = L [/itex] ? I'm actually using this as a lemma in one of my other proofs (the proof that the nth term of a convergent sum approaches 0), but can't get around the proof of this not-so-obvious-but-still-quite-intuitive lemma.(adsbygoogle = window.adsbygoogle || []).push({});

I wrote down the Cauchy-definitions of both these limits, but have no idea how to deduce one from the other.

Thanks for all the help!

BiP

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# Infinite series question

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