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Math Help - subtraction series from each other

  1. #1
    da`
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    subtracting series from each other

    I am working on cauchy criterion and I am trying to show that a series converges to a limit. After showing basic proofs, i am trying to relate this to my case.

    Now is the following that I have done correct?

    Thanks for any help,

    ps. Apologies for the infractions.
    Attached Thumbnails Attached Thumbnails subtraction series from each other-432432.jpg  
    Last edited by da`; April 22nd 2009 at 03:15 PM. Reason: spelling mistake in title
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  2. #2
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  3. #3
    da`
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    Sorry.

    I have attached my question below. I am trying to show the convergence and giving Cauchy's Convergence Criterion. So I have defined Sn and Sm as you can see in the original attachment.

    Part of the process is to take both sequences away from each other within the modulos. I am wondering if I have managed to take both sequences away from each other successfully.

    Thanks
    Attached Thumbnails Attached Thumbnails subtraction series from each other-6666666.jpg  
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