Let
$$S_n = \sum_{k=1}^{n}\frac{n}{n^2 + kn + k^2}$$ and $$T_n = \sum_{k=0}^{n-1}\frac{n}{n^2 + kn + k^2}$$, for $$n = 1, 2, 3, ..., $$ Then,

A

$$S_n < \frac{\pi}{3\sqrt{3}}$$

B

$$S_n > \frac{\pi}{3\sqrt{3}}$$

C

$$T_n < \frac{\pi}{3\sqrt{3}}$$

D

$$T_n > \frac{\pi}{3\sqrt{3}}$$