(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Moessner's Theorem states:

Begin with the ordered list of all positive integers.

Cross out every nth element, and take the prefix sum of the sequence resulting.

Cross out every (n-1)th element of this new seqence, and take the prefix sum.

Repeat until you would have to remove every element. The final sequence is a list of x^n.

2. Relevant equations

Not sure.

3. The attempt at a solution

Well, n=1 is trivial and n=2 can be proven via

Ʃ^{a}_{n=1}(2n-1) = 2(0.5n(n+1))-n = n^{2}

I'm not sure how to make a general case though. Also, I noticed I can get factorials by increasing the size of the steps; I'm guessing the proof of this would be similar to the proof of powers though.

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# How does Moessner's Theorem work?

Can you offer guidance or do you also need help?

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