# Ryan's function composition

Algebra Level 4

If $$f(x)= \frac {x-1}{x}$$ and $$g(x)= \frac {3x+1}{3-9x}$$, what is the value of

$\displaystyle \sum_{k=1}^{2520} \left(f^{k}(2)-g^{k}(2) \right)?$

This problem is posed by Ryan P.

Details and assumptions

Note: $$f^{k}(x)$$ denotes the composition of the function $$k$$ times. For example, $$f^2(x) = f(f(x))$$.

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