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