This is a short, animated visual proof demonstrating the finite geometric sum formula for any integer n with n greater than 3 (explicitly showing the case n=6 with k=3). This series (and its infinite analog when x less than 1) is important for many results in calculus, discrete mathematics, and combinatorics.
To buy me a coffee, head over to https://www.buymeacoffee.com/VisualPr...
Thanks!
For a longer version of this video with other geometric sums (to see how this generalizes), check out: • Self Similar Geometric Series: Sums o...
Also, check out my playlist on geometric sums/series: • Geometric Sums
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 #calculus #mtbos #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #finitesums #finiteseries #geometric #mathshorts #mathvideo
To learn more about animating with manim, check out:
https://manim.community
Watch video Summing Powers of 6 (geometric sum visualization) online without registration, duration hours minute second in high quality. This video was added by user Mathematical Visual Proofs 20 May 2024, don't forget to share it with your friends and acquaintances, it has been viewed on our site 43,615 once and liked it 1.9 thousand people.