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Math Help - cauchy subsequence question

  1. #1
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    cauchy subsequence question

    A sequence  (x_n) has a Cauchy subsequence if and only if it has a subsequence (x_n_k) for which d(x_n_k,x_n_{k+1}) < 2^{-k}
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: cauchy subsequence question

    Quote Originally Posted by wopashui View Post
    A sequence  (x_n) has a Cauchy subsequence if and only if it has a subsequence (x_n_k) for which d(x_n_k,x_n_{k+1}) < 2^{-k}
    what have you tried, once again? This one is slightly tricky, the key thing to note is that \displaystyle \sum2^{-k}=1. So, use the triangle inequality, etc.
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