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What is the sum of all areas shaded in blue in the following figure?

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What is the sum of all areas shaded in blue in the following figure?
The areas are constructed as follows. Start with a unit square and inscribe a circle. The area between the circle and the square is the first area. In each subsequent step, inscribe a new square inside the previous circle and then inscribe another circle inside the new square. In each step shade the area between the circle and the square. The question is to find the sum of all such areas if the steps are repeated infinitely.
enter image description here

posted Jul 14 by Pushpak Chauhan

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