Function Frenzy

Level pending

Let \(f(x)=\frac{2^{2x}}{2^{2x}+2}\) for every \(x \in \mathbb{R}\). What is the value of \(\left \lfloor \sum_{n=1}^{2013}f\left(\frac{n}{2014}\right) \right \rfloor\)?

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