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 $\lfloor S \rfloor + 2016$ .