# That's a Parabola!

Geometry Level 5

Consider a Parabola

$y = \frac{x^{2}}{4}$

With vertex 'O'

And a point F(0 , 1)

Let $$B_1( x_1 , y_1 ) , B_2( x_2 , y_2 ) \ldots B_n( x_n , y_n )$$

are 'n' points on the Parabola

Such that $$x_k > 0$$ and

$$\displaystyle \angle OFB_k = \frac{ k \pi}{2n}$$ ( k = 1, 2, 3 $$\ldots$$ , n)

Then find the value of

$\lim_{ n \to \infty } \frac{1}{n} \sum_{k = 1}^{n} FB_k$

upto 3 decimal place

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