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Math Help - Two convergent subsequences, divergent sequence

  1. #1
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    Feb 2009
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    Two convergent subsequences, divergent sequence

    I know that if a sequence has two subsequences that converge to different values than that sequence is divergent. However, I am asked to prove this fact. Any help is much appreciated.
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  2. #2
    Junior Member
    Joined
    Sep 2011
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    Re: Two convergent subsequences, divergent sequence

    The basic setup is to let two subsequences converge to two different values. Then to show the sequence doesn't converge, take a particular epsilon and show that you for all N sufficiently huge you can't be close to one limit value because you must be hitting the limits of the subsequences

    Can you see a good epsilon to choose?
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