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Is there a general formula for the above summation (in terms of $r$ and $k$)? I've read a very helpful answer on the general formula for $\sum_{n=1}^{\infty} n r^n$, and according to this answer, there was a general formula for arbitrary $k$; however, I couldn't find any references in there as to what it was.

Thanks in advance, all your help is greatly appreciated!

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