Self Similar Geometric Series: Sums of powers of 7 (and all integers larger than 3)

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 cases n=7 and n=9 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. #manim​ #math #geometricsums #series​ #calculus #mtbos​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #finiteseries #geometric #mathshorts​ #mathvideo​

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Music in this video:
Creative Commons Attribution 3.0 Unported License

[BariScienceLab]

You’re great! Keep doing what you do. I have understood several math concepts better because of your videos!

[mathflipped]

Interesting visual proof! I've never seen this kind of equality before.

[MrParry]

Amazing! Looks almost like a fractal which makes it even more attractive!

[LorvinWolf]

1:20 looks like a just shapes and beats boss

[Nathouuuutheone]

Many of your videos lack context. Any chance you can introduce what you're doing before starting your animations? It's real cute but what IS it??

[wcdeich]

Do you have any idea how I could draw the Barnsley fern with edge lines instead of fill-in dots?

[SsoUuLl]

Educational and beautiful, but music makes me think that we've just witnessed the invention of a cold fusion reactor

[theskinegg]

why does n have to be greater than 3, can’t it work for all numbers