Infinite Number of Cubes inside a Cube

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A series of cubes are aligned along the diagonals of a cube. Each cube has edge length half the size of the previous cube's edge length and its center is at a vertex of the previous cube. The enveloping cube is shown as a skeleton; half of its edge length is . No matter how large is, . This is one way to see that the sum of the infinite series is 1.

Contributed by: Sándor Kabai (May 2008)
Open content licensed under CC BY-NC-SA


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