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 \(\lfloor 10000 \times S \rfloor \).


Happy Birthday to you Swapnil and Sharky. This problem is dedicated to you guys.
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