Sum of Reciprocals of Triangular Numbers

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The sum of the reciprocals of the triangular numbers is



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


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



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

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