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Need critique and proof of a theorem

  1. Feb 26, 2008 #1
    Can anyone prove the next theorem, if it's new I think it's mine.
    Thank you for trying.


    a en b are integers a>0, b>0

    [tex]X1[/tex] f(1) =a
    [tex]X2[/tex] f(n+1) = (2f(n))mod(a+b)

    \lim_{n\rightarrow\infty}\sum_{k=1}^{n}|{f(k+1)-f(k)}|\left(\frac{1}{4}\right)^k = \frac{ab}{2(a+b)}
  2. jcsd
  3. Feb 26, 2008 #2
    In Mathematica I can give different values for a and b, like a=8, b=9 and this is not a counterexample. n must be a large number like n=50 or n=100. If there is a single counterexample then this is enough to prove the theorem is wrong.
  4. Feb 26, 2008 #3
    Nice observation, I don't know if this is already known. Anyways it seems to be true:smile:

    How did you come up with that?
  5. Feb 26, 2008 #4
    HB - I erased my post very shortly after making it as I realized in my program I had the formulas all wrong. I now have it correctly entered and It appears to be true for all a and b up to 10k (not that that means it will always be true :wink:)
  6. Feb 28, 2008 #5
    Pere, I came up with the theorem when I defined a physical formula about kinetic energy.
    I think this is not the right forum to start a discussion about this.
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