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Theorem (2)

  1. May 11, 2009 #1
    This theorem (if it is proven) comes also from a formula of kinetic energy.
    Has anyone some suggestions about this one.

    Definition of f(n):

    [tex]
    \ f(n)=(2^{n-1}a)Mod(a+b)
    [/tex]

    Definition of g(n):

    [tex]\
    \ g(n)= 4f(n)-2(a+b)+1
    [/tex]

    Definition of h(n):

    [tex]
    \ h(n)= Sign(f(n))(Sign(g(n))+1)
    [/tex]

    Theorem:

    [tex]
    \lim_{n\rightarrow\infty}\sum_{k=1}^{n}{h(k)\left(\frac{1}{2}\right)^{k+1}} = \frac{a}{(a+b)}
    [/tex]

    Thank you for trying.
     
  2. jcsd
  3. May 11, 2009 #2
    n, a and b are integers > 0
     
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