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Problems > The Maine Page > 2002

A Sequence of Circles

I have an infinite number of circles. The first one has radius r. The second has radius r/2. The third has radius r/4, and so on.

I also have an infinite number of squares, each of which has area equal to the area of the corresponding circle.

What is the sum of the perimeters of all my squares?

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X, Y, and Z
Fractional Infinite Series

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