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

• ①$\displaystyle \frac{4} {e}$
• ②$\displaystyle \frac{e} {2}$
• ③$\displaystyle \frac{e} {4}$
• ④$\displaystyle \frac{2} {e}$