A relevant summation

Calculus Level 5

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

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

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