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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