Funny functions

Algebra Level 3

\[ \large f \left(\frac{1}{2009} \right)+f\left(\frac{2}{2009}\right) +f\left(\frac{3}{2009}\right) + \ldots +f\left(\frac{2008}{2009}\right) \]

Let \(\large f(x)=\dfrac{4^{x}}{4^{x}+2}\), find the value of the expression above.

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