# Calculus + Geometry??

Geometry Level 5

Consider a parabola $$x^2=4y$$ and the point $$F= (0,1)$$. Let $$A_1 = (X_1, Y_1) , A_2 = (X_2 , Y_2) , \ldots , A_n = (X_n , Y_n)$$ denote the $$n$$ points on the parabola such that $$X_k> 0$$ and $$\angle OFA_k = \dfrac{k\pi }{2n}$$ for $$k = 1,2,3,\ldots, n$$.

Compute $$\displaystyle \lim_{n\to\infty} \dfrac1n \sum_{k=1}^n FA_k$$.