Kenny's Identity

Calculus Level 4

\[L=\lim_{x\to0}\sum_{n=1}^{\infty}\sum_{r=0}^{\infty}\frac{(-1)^r}{n+r}\dbinom{n+r}{r}x^{n+r-1}\]

Find the value of \(\lfloor10000L\rfloor\).


This problem is original.
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