$\displaystyle \lim _ {n \rightarrow \infty} {} \sum _ {k=1} ^ {n} \frac{1-2a} {n} \left \{2a+ \frac{(1-2a) k} {n} \right \} ^ {2}$ 의 값은? (단, $\displaystyle 0<a< \frac{1} {2}$)

• ①$\displaystyle \frac{1} {3} \left (1-a^ {3} \right)$
• ②$\displaystyle \frac{1} {3} \left (1-8 a^ {3} \right)$
• ③$\displaystyle \frac{8} {3} \left (1-a^ {3} \right)$
• ④$\displaystyle \frac{1} {3} \left (8-a^ {3} \right)$