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Sum of Reciprocals of Triangular Numbers

The sum of the reciprocals of the triangular numbers is
.
For each , the area of each colored rectangle in the graphic is .

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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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"Sum of Reciprocals of Triangular Numbers" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/SumOfReciprocalsOfTriangularNumbers/
Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa




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