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Math Help - Double Sum

  1. #1
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    Double Sum

    OK, last problem. What is \sum_{n=0}^{\infty} (-1)^n\sum_{k=0}^{n} n!/(n-k)!* ln^{n-k}(2)? Could I combine the sums? I am unsure of how to, though.
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  2. #2
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    Combine?! Why would you want to do that?

    You can pull out the "n!" and the \ln^{n}(2).

    That might give you somewhere to go.

    1) Does the inner-sum converge?
    2) Does the alternating sign out front make it any better?
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  3. #3
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    Double Sum

    I am getting that the sum goes to infinity- is this right?
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  4. #4
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    If you mean, "Increases Without Bound", that could be closer.
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