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Thread: Cauchy's criteria of uniform convergence of series

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    Cauchy's criteria of uniform convergence of series

    How to prove Cauchy's criteria of uniform convergence of series using same Cauchy's criteria for sequence of functions.
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    |S_{n+p}-S_n|=|f_{n+1}+...+f_{n+p}|... now what...?
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  2. #2
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    Quote Originally Posted by Also sprach Zarathustra View Post
    How to prove Cauchy's criteria of uniform convergence of series using same Cauchy's criteria for sequence of functions.
    .
    .
    .

    |S_{n+p}-S_n|=|f_{n+1}+...+f_{n+p}|... now what...?
    I don't really get what the difficulty is, just take the sequence of partial sums and apply the theorem for sequences.
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