1. ## Double 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.

2. 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?

3. ## Double Sum

I am getting that the sum goes to infinity- is this right?

4. If you mean, "Increases Without Bound", that could be closer.