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Can you attack this function?

Algebra Level 4

If $f(x)=\frac{4^x}{4^x+2}$ , where $x€Q$ , then $f(\frac{1}{2007})+f(\frac{2}{2007})+...+f(\frac{2006}{2007})$ equals to $?$

2015 none of them 2016 1999 1003 2007

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by Atul Shivam

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