Welcome 2016! Part 17

Algebra Level 4

\[\large S= \dfrac{2^2+1}{2^2-1}+\dfrac{3^2+1}{3^2-1}+ \ldots + \dfrac{2016^2+1}{2016^2-1}\]

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