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Sum of a Geometric Series

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All the green triangles are similar, and the big triangle is similar to the green triangles.

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The ratio of the big triangle's sides is equal to the ratio of the sides for those triangles, so that , and then .

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Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa (March 2011)
Open content licensed under CC BY-NC-SA

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Reference: J. H. Webb, "Proof without Words: ," Mathematics Magazine, 60(3), 1987 p. 177.

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