Be Positive in 2017

Algebra Level 4

f(2017)+f(2016)+f(2015)++f(4)+f(3)+f(2)+f(12)+f(13)+f(14)++f(12015)+f(12016)+f(12017) f(2017) + f(2016) + f(2015) +\cdots + f(4) + f(3) + f(2) + f \left(\frac{1}{2}\right) + f\left(\frac{1}{3}\right) + f\left(\frac{1}{4}\right) + \cdots + f\left(\frac{1}{2015}\right) + f\left(\frac{1}{2016}\right) + f\left(\frac{1}{2017}\right)

Given that ff is a real function such that f(x)=x1x f(x) = \dfrac{x}{1-x} for x1 x \neq 1 . Find the value of the expression above.


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