Limit problem

Calculus Level 3

If \[L=\displaystyle\lim \limits_{n\to \infty }\frac{1}{n} \displaystyle\sum \limits^{n}_{j=1}\cos \left( \frac{j\pi }{2n} \right) \] find \(\left\lfloor \frac{1}{L}\right\rfloor \).

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