# Waiting for 2016!

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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