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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"Infinite Number of Cubes inside a Cube"
http://demonstrations.wolfram.com/InfiniteNumberOfCubesInsideACube/
Wolfram Demonstrations Project
Published: May 30 2008