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Thank you for trying.

Definition

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)

Theorem

[tex]

\lim_{n\rightarrow\infty}\sum_{k=1}^{n}|{f(k+1)-f(k)}|\left(\frac{1}{4}\right)^k = \frac{ab}{2(a+b)}

[/tex]