JEE Math Practice Question

$$\mathop {\lim }\limits_{n \to \infty } \left( {{{{n^2}} \over {({n^2} + 1)(n + 1)}} + {{{n^2}} \over {({n^2} + 4)(n + 2)}} + {{{n^2}} \over {({n^2} + 9)(n + 3)}} + \,\,....\,\, + \,\,{{{n^2}} \over {({n^2} + {n^2})(n + n)}}} \right)$$ is equal to :

1. A.$${\pi \over 8} + {1 \over 4}{\log _e}2$$
2. B.$${\pi \over 4} + {1 \over 8}{\log _e}2$$
3. C.$${\pi \over 4} - {1 \over 8}{\log _e}2$$
4. D.$${\pi \over 8} + {\log _e}\sqrt 2 $$