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

Give your answer to 2 decimal places.

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