Uploads from Mathematical Visual Proofs

Currently Playing: Abel Sum of Grandi’s Series

Abel Sum of Grandi’s Series We show how an amazing visual proof of the infinite alternating geometric series formula for any positive ratio r with r less than 1 allows us to make sense of one particular Abel sum assignment of a value to a famous divergent series. To buy me a coffee, head over to https://www.buymeacoffee.com/VisualProofs Thanks! To see the original alternating series proof short, check out : https://youtube.com/shorts/ttSl8bMmwKA?feature=share For a slower, wide format version of the alternating series proof (without words), see https://youtu.be/Qa0bOHYjnW0 Also, check out my playlist on geometric sums/series: https://youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw This animation is based on a proof by The Viewpoints 2000 group from the October 2001 issue of Mathematics Magazine page 320 (https://www.jstor.org/stable/2691106 ). ​​ #math​ #calculus​ #manim​ ​ #abelsum #divergentseries To learn more about animating with manim, check out: https://manim.community