Think about the expansion, it is not small

Calculus Level 4

$\large \displaystyle L=\lim_{n \to \infty} \sum_{k=1}^{n} \dfrac{n-k}{n^2} \cos\left(\dfrac{4k}{n}\right)$

Find the value of $$\lfloor 1000L \rfloor$$.

×