This is a short, animated visual proof demonstrating the infinite geometric series formula for any positive ratio r with r less than 1. This series is important for many results in calculus, discrete mathematics, and combinatorics. #mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries

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This animation is based on a proof by Benjamin G. Klein and Irl C. Bivens from the October 1988 issue of Mathematics Magazine page 219 ([ Ссылка ]).

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