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Proofs Without Words

The Series of Reciprocals of Triangular Numbers

Page 572 | Received 25 Jan 2020, Accepted 22 Sep 2020, Published online: 05 Oct 2022
 

Abstract

We provide a visual proof that the infinite sum of the reciprocals of the triangular numbers is 1. Such visual proofs usually stack line segments or rectangular blocks. Here we stack angles.

Additional information

Notes on contributors

Paul Stephenson

Paul Stephenson taught mathematics and physics for two decades before creating a touring math lab structured around the multiple embodiment principle of the late Z. P. Dienes. The Magic Mathworks Traveling Circus, registered in the U. K. as a not-for-profit company, has now been on the road for thirty years.

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