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Algebra Level 5

Given that \(f(x) = \dfrac{25^x}{25^x + 5} \). If the value of the sum, \( \displaystyle \sum_{a=1}^{2015} f \left(\dfrac a{2016} \right) \) is equal to \(\dfrac AB\), where \(A\) and \(B\) are coprime positive integers, find the value of \(A+B\).

Hint: Generalize this.

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