$\displaystyle \lim _ {n \rightarrow \infty} {{\left (\frac{8} {n} + \frac{8n} {n^2 +1} + \frac{8n} {n^2 +4} + \frac{8n} {n^2 +9} + \cdots + \frac{8n} {2n^2 -2n+1} \right)}}$ 의 값은?

• ①$\pi$
• ②$2 \pi$
• ③$3 \pi$
• ④$4 \pi$
• ⑤$5 \pi$