Sum of a Geometric Series

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 .

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

US Common Core State Standards, Mathematics