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

If every subsequence of the sequence a_n converges to 0, prove that a_n itself converges to 0. Is the converse true? Prove it or give a counter example.

2. Relevant equations

3. The attempt at a solution

I can prove a sequence is convergent if it has a convergent subsequence. What about every sequence is convergent?

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# Homework Help: Sequence and covvergence

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