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Currently Playing: A Self Similar Sum (Powers of 3) Proof without Words

A Self Similar Sum (Powers of 3) Proof without Words This is a short, animated visual proof demonstrating the finite geometric sum formula for any integer k with k greater than 3 (explicitly showing the case n=3 and k=3). This series (and its infinite analog when x less than 1) is 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/VisualProofs. or join my Patreon: https://www.patreon.com/c/MathVisualProofs For a longer version of this video with other geometric sums (to see how this generalizes), check out: https://youtu.be/1wIdJxSfUz4 Also, check out my playlist on geometric sums/series: https://youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw This animation is based on a proof by Mingjang Chen from the December 2004 issue of Mathematics Magazine page 373 (https://doi.org/10.2307/3219202). #manim​ #math #geometricsums #series​​ ​#proofwithoutwords​ To learn more about animating with manim, check out: https://manim.community