JEE Math Practice Question

$$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{r \over {2{r^2} - 7rn + 6{n^2}}}} $$ is equal to :

1. A.$${\log _e}\left( {{{\sqrt 3 } \over 2}} \right)$$
2. B.$${\log _e}\left( {{{3\sqrt 3 } \over 4}} \right)$$
3. C.$${\log _e}\left( {{{27} \over 4}} \right)$$
4. D.$${\log _e}\left( {{4 \over 3}} \right)$$