Geometric sum of powers of 7

Описание: 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=7 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 of pow...  

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