Infinite Sum of Powers of 1/3 in Equilateral Triangle @MathVisualProofs

Uploaded March 2026 | Updated September 2026, 2 weeks ago

Infinite Sum of Powers of 1/3 in Equilateral Triangle

This is a short, animated visual proof demonstrating the sum of an infinite geometric series using a dissection proof in an equilateral triangle. In particular, we show how to find the sum of powers of 1/3 in the equilateral triangle. Geometric series are important for many results in calculus, discrete mathematics, and combinatorics.

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Also, check out my playlist on geometric sums/series: youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw

This animation is based on a proof by Stephan Berendonk (2020) from the November 2020 issue of The College Mathematics Journal, (doi.org/10.1080/07468342.2020.1830649 p. 385)

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