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A square has sides of 10 inches each. A second square is inscribed in the original...

A square has sides of 10 inches each. A second square is inscribed in the original square by joining the midpoints of the sides, as shown below. A third square is then inscribed inside the second square by joining the midpoints of the sides of the second square. This process is continued endlessly. What is the sum of the areas of the infinite sequence of squares?

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