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Math Help - Cauchy sequence

  1. #1
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    Cauchy sequence

    Prove that every convergent sequence is a Cauchy sequence.

    [SOLVED] I will post my result if anyone is curious.

    Thanks
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  2. #2
    Super Member malaygoel's Avatar
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    I would like to see your result
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  3. #3
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    Suppose a_{n} \rightarrow a.

    \forall \epsilon > 0, \exists N : |a_{n} - a| < \epsilon/2 ,  \forall k> N. Then,

    |a_{n} - a_{m}| = |a_{n} - a + a - a{m}|

    Which is, < |a_{n} - a| + |a - a_{m}|

    Which is, < \epsilon/2 + \epsilon/2 = \epsilon \forall n,m > N.

    I recently discovered how to overuse quantifiers
    Last edited by cgiulz; October 1st 2009 at 08:51 AM.
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