Euler's count of circle pieces

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The function \( R(n) \) denotes the maximum number of areas which can be formed within the circle when all chords between \( n \) distinct points on a circle are drawn.

In the figures above we see that \( R(2) = 2, R(3) = 4 \) and \( R(4) = 8 \).


Find the smallest value of \( R(n) \geq 1000 \).

Note: The \( n \) points lie on the circle in such a way that the 'maximum' number of areas are formed.

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