$\displaystyle \lim _ {n \rightarrow \infty} {\frac{1} {n^2} \sum _ {k=1} ^ {n} k \cos ^3 \left (\frac{\pi k^2} {6n^2} \right)}$ 의 값은?

• ①$\displaystyle \frac{11} {10} \pi$
• ②$\displaystyle \frac{11} {8} \pi$
• ③$\displaystyle \frac{11} {6} \pi$
• ④$\displaystyle \frac{11} {4} \pi$
• ⑤$\displaystyle \frac{11} {2} \pi$