# Be Positive in 2017

Algebra Level 4

$f(2017) + f(2016) + f(2015) +\cdots + f(4) + f(3) + f(2) + f \left(\frac{1}{2}\right) + f\left(\frac{1}{3}\right) + f\left(\frac{1}{4}\right) + \cdots + f\left(\frac{1}{2015}\right) + f\left(\frac{1}{2016}\right) + f\left(\frac{1}{2017}\right)$

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

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