$\displaystyle\lim_{n \to \infty} \begin{bmatrix}\frac{1}{n+1} + \frac{1}{n+2} + ... +\frac{1}{2n} \end{bmatrix} $ is equal to :

Question

( A ) $\log 4$
( B ) $\log 3$
( C ) $\log 2$
( D ) $\frac{\pi}{2}$