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Given that f(x)=25x25x+5f(x) = \dfrac{25^x}{25^x + 5} f(x)=25x+525x. If the value of the sum, ∑a=12015f(a2016) \displaystyle \sum_{a=1}^{2015} f \left(\dfrac a{2016} \right) a=1∑2015f(2016a) is equal to AB\dfrac ABBA, where AAA and BBB are coprime positive integers, find the value of A+BA+BA+B.
Hint: Generalize this.
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