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Three Geometric Series in an Equilateral Triangle (visual proof without words)

This is a short, animated visual proof demonstrating the sum of three infinite geometric series using dissection proofs in an equilateral triangle. In particular, we show how to find the sum of powers of 1/2, of powers of 1/3 and of powers of 1/7 in the equilateral triangle. Geometric series are important for many results in calculus, discrete mathematics, and combinatorics. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualPr.... Thanks! Also, check out my playlist on geometric sums/series:    • Geometric Sums   This animation is based on a proof by Stephan Berendonk (2020) from the November 2020 issue of The College Mathematics Journal, (https://doi.org/10.1080/07468342.2020... p. 385) #mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries #equilateraltriangle To learn more about animating with manim, check out: https://manim.community ______________________________ Music in this video: Reaching The Sky (Long Version) by Alexander Nakarada (CreatorChords) | https://creatorchords.com Music promoted by https://www.free-stock-music.com Creative Commons / Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/...