극한 $\displaystyle \lim _ {n \rightarrow \infty} {\frac{(1^2 +2^2 + \cdots + n^2) (1^3 +2^3 + \cdots +n^3)} {(1+2+ \cdots +n) (1^4 +2^4 + \cdots +n^4)}}$ 의 값은?

• ①$\displaystyle \frac{5} {6}$
• ②$\displaystyle \frac{6} {5}$
• ③$\displaystyle \frac{6} {7}$
• ④$\displaystyle \frac{7} {6}$