Cyclic Regular Polygon Fractals

Calculus Level 3

The nthn^{\text{th}} figure in the above sequence is constructed by the following procedure:

  1. Draw a blue disc of radius 2016π\displaystyle\sqrt{\frac{2016}{\pi}}
  2. Remove a regular nn-gon area from the (smallest) disc
  3. Inscribe a blue disc inside the empty nn-gon space
  4. Repeat steps 2-4

Let AnA_n be the total blue area of the nthn^{\text{th}} figure in the sequence.

Compute limnAn\displaystyle\lim_{n\to\infty}A_n.

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