OK, last problem. What is $\displaystyle \sum_{n=0}^{\infty} (-1)^n\sum_{k=0}^{n} n!/(n-k)!* ln^{n-k}(2)$? Could I combine the sums? I am unsure of how to, though.

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- Jan 30th 2010, 10:40 AMPaulDirac2Double Sum
OK, last problem. What is $\displaystyle \sum_{n=0}^{\infty} (-1)^n\sum_{k=0}^{n} n!/(n-k)!* ln^{n-k}(2)$? Could I combine the sums? I am unsure of how to, though.

- Jan 30th 2010, 12:44 PMTKHunny
Combine?! Why would you want to do that?

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

That might give you somewhere to go.

1) Does the inner-sum converge?

2) Does the alternating sign out front make it any better? - Jan 30th 2010, 02:14 PMPaulDirac2Double Sum
I am getting that the sum goes to infinity- is this right?

- Jan 30th 2010, 02:37 PMTKHunny
If you mean, "Increases Without Bound", that could be closer.