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Algebra Level 5

Given that f(x)=25x25x+5f(x) = \dfrac{25^x}{25^x + 5} . If the value of the sum, a=12015f(a2016) \displaystyle \sum_{a=1}^{2015} f \left(\dfrac a{2016} \right) is equal to AB\dfrac AB, where AA and BB are coprime positive integers, find the value of A+BA+B.

Hint: Generalize this.

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