Demonstration of 0.66666… = 1 in Base 7 Using Infinite Series

This is a short, animated visual proof showing the sum of the infinite geometric series with first term 6/7 and ratio 1/7, which in turn allows us to compute the sum of the series of powers of 1/7 and determine an interesting base 7 representation of 1. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! For a longer, wordless version of this animation with two other proofs, see https://youtu.be/L-pxcCk3Xi4?si=hCnLn61vVxSOp2b4 Also, check out my playlist on geometric sums/series: https://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, (https://doi.org/10.1080/07468342.2020.1830649 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