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The hardest ever

  1. Apr 11, 2009 #1
    The hardest ever,,,

    1. The problem statement, all variables and given/known data

    40) for which positive intigers k is the following sries convergent:
    (n!) ^2 / (kn)!

    2. Relevant equations

    using the ratio test the limit should be less than 1

    3. The attempt at a solution

    I tried the ratio test, but I got inifinty?
     
  2. jcsd
  3. Apr 11, 2009 #2

    tiny-tim

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    Hi remaan! :smile:
    Hint: which is larger, (5!)2 or 10! ? :wink:
     
  4. Apr 11, 2009 #3

    Hurkyl

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    Re: The hardest ever,,,

    No -- it could be less than 1, but it doesn't have to. You're making some assumptions when you said that; what are they? (Or, I suppose you could have just made a mistake)

    What does that tell you?
     
  5. Apr 11, 2009 #4
    Re: The hardest ever,,,

    Hi,

    mm, 1o! is greater, but how can I benifit from this in finding K ??
     
  6. Apr 11, 2009 #5
    Re: The hardest ever,,,

    It tells that the series is not alternating and I can't ( ratio test ) to find the k .
     
  7. Apr 11, 2009 #6

    Hurkyl

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    Re: The hardest ever,,,

    Why not? The only time the ratio test is inconclusive is when the limit is 1, or doesn't exist, and for all possible values of k, you're not in either of those cases
     
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