(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If {s_n} is a Cauchy sequence of real numbers which has a subsequence converging to L, prove that {s_n} itself converges to L.

2. Relevant equations

3. The attempt at a solution

I know that all Cauchy sequences are convergent, and I know that any subsequences of a convergent sequence are convergent to the same limit as the sequence, but I am not sure if I can turn the second part of the statement around to say that if a subsequence is convergent to L, then the sequence converges to the same limit. Any ideas? Thanks.

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# Homework Help: Cauchy sequence proof

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