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.


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


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



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

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