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

Suppose that {Xn} is a sequence inR. Prove that Xn converges to a if and only if every subsequence of Xn converges to a.

2. Relevant equations

3. The attempt at a solution

Let e>0, choose N inNst n >=N implies |Xn-a| <e. Since a subsequence, nk, is inNand n1<n2<n3...., then nk>=k for all k inN. So, k>= implies |Xnk-a|<e.

That's the first part, but I can't figure out how to start the proof the other way around. i.e. how do you prove that a convergent subsequence implies a convergent sequence?

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# Homework Help: Subsequence Convergence

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