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How does Moessner's Theorem work?

  1. Jan 12, 2012 #1
    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
    Ʃan=1 (2n-1) = 2(0.5n(n+1))-n = n2
    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.
  2. jcsd
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