300 Followers Problem - To my friends Swapnil and Sharky

Calculus Level 4

\[\large S = \dfrac{1}{1\times 2^2} + \dfrac{1}{2 \times 3^2} + \dfrac{1}{3 \times 4^2} + \cdots\]

Find the value of \(\lfloor 10000 \times S \rfloor \).