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Math Help - Cauchy Sequences

  1. #1
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    Cauchy Sequences

    I am asked to show that the following is a Cauchy sequence from the definition of a Cauchy sequence.

    (1 + 1/(2!) + ... + 1/(n!))


    I'm not really sure how to deal with the factorial. Any help would be much appreciated.
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  2. #2
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    Quote Originally Posted by jkru View Post
    I am asked to show that the following is a Cauchy sequence from the definition of a Cauchy sequence.

    (1 + 1/(2!) + ... + 1/(n!))


    I'm not really sure how to deal with the factorial. Any help would be much appreciated.
    Try proving this. If |a_{n+1}-a_n| \leq b_n and \sum_{n=1}^{\infty} b_n < \infty then \{ a_n\} is Cauchy.
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