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Convergent series

  1. Feb 16, 2010 #1
    Given a sequence, how does one prove that the associated series in convergent or not, in a given norm? For example,

    [tex]\sum_{k=0}^{\infty}a_{k} [/tex] in [tex]||\cdot|| [/tex]

    The process to do this is not in my book; I'm told how to determine whether a series is cauchy, but I'm not sure how to use that to show it's convergent.
     
  2. jcsd
  3. Feb 16, 2010 #2
    depending on the series there will be a different method for proof of convergence or divergence. is there a specific series you are speaking of?
     
  4. Feb 16, 2010 #3
    I have several, in several spaces.

    [tex] f_{n}(t) \ in \ (C[0,1],||\cdot||_{\infty}) [/tex]

    is an example of one.
     
  5. Feb 16, 2010 #4
    got nothing for you man. sorry.
     
  6. Feb 16, 2010 #5
    I don't even understand your notation. good luck though
     
  7. Feb 17, 2010 #6
    bump, can someone please give this another look? I'd like to work these problems, but my book is not helpful and my campus is closed this week :(

    If there is no help, can a moderator move this post into the Homework Help Forum?
     
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