Welcome 2016! Part 17

Algebra Level 4

S=22+1221+32+1321++20162+1201621\large S= \dfrac{2^2+1}{2^2-1}+\dfrac{3^2+1}{3^2-1}+ \ldots + \dfrac{2016^2+1}{2016^2-1}

If SS denotes the value of the above expression, then find the value of S+2016\lfloor S \rfloor + 2016 .

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