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S=22+122−1+32+132−1+…+20162+120162−1\large S= \dfrac{2^2+1}{2^2-1}+\dfrac{3^2+1}{3^2-1}+ \ldots + \dfrac{2016^2+1}{2016^2-1}S=22−122+1+32−132+1+…+20162−120162+1
If SSS denotes the value of the above expression, then find the value of ⌊S⌋+2016\lfloor S \rfloor + 2016⌊S⌋+2016 .
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