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Let {Cn} be an infinite sequence of circles lying in the positive quadrant of the XY-plane, with strictly decreasing radii and satisfying the following

 

Let {Cn} be an infinite sequence of circles lying in the positive quadrant of the XY-plane, with strictly decreasing radii and satisfying the following conditions. Each C, touches both the X-axis and the Y-axis. Further, for all n > 1, the circle Cn+1 touches circle Cn externally. If C1 has radius 10 cm, then show that the sum of the areas of all these circles is 25n/(3V2 - 4).

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