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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.