$ \displaystyle{\lim_{x \to \infty} [\frac{1}{n^2} \sec^2 \frac{1}{n^2} + \frac{2}{n^2} \sec^2 \frac{4}{n^2} + . . . . . . + \frac{n}{n^2} \sec^2 1]}$

Question

( A ) $\frac{1}{2} \mathrm{cosec}\; 1$
( B ) $\frac{1}{2} \sec \;1 $
( C ) $\tan \;1$
( D ) $\frac{1}{2} \tan \;1$