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

• ①$\displaystyle \frac{16} {25}$
• ②$\displaystyle \frac{25} {64}$
• ③$\displaystyle \frac{49} {64}$
• ④$\displaystyle \frac{25} {81}$
• ⑤$\displaystyle \frac{25} {49}$