A relevant summation

Calculus Level 5

1(1)(2)(3)+2(4)(5)(6)+3(7)(8)(9)+4(10)(11)(12)+\large\displaystyle\dfrac{1}{(1)(2)(3)}+\dfrac{2}{(4)(5)(6)}+\dfrac{3}{(7)(8)(9)}+\dfrac{4}{(10)(11)(12)}+\ldots

Let S\large S denote the value of series above. Find the value of 10000S\large\lfloor10000S\rfloor.

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