Sum of Reciprocals of Triangular Numbers

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The sum of the reciprocals of the triangular numbers is

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For each , the area of each colored rectangle in the graphic is .

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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: R. B. Nelsen, "Proof without Words: Sum of Reciprocals of Triangular Numbers," Mathematics Magazine, 64(3), 1991 p.167.



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