$\displaystyle \lim _ {n \rightarrow \infty} \frac{1} {n ^ {3}} \left (\sqrt {\frac{1} {n}} + 2 ^ {2} \sqrt {\frac{2} {n}} + 3 ^ {2} \sqrt {\frac{3} {n}} + \cdots + n ^ {2} \sqrt {\frac{n} {n}} \right)$ 의 값은?

• ①$\displaystyle \frac{1} {2}$
• ②$\displaystyle \frac{2} {5}$
• ③$\displaystyle \frac{1} {3}$
• ④$\displaystyle \frac{2} {7}$