The Geometry of Finite Geometric Sums (visual proof; series)

This is a short, animated visual proof demonstrating the finite geometric for any ratio x with x greater than 1. This series (and its infinite analog when x less than 1) is important for many results in calculus, discrete mathematics, and combinatorics. #mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #geometricsums #series #finitesums #finiteseries #geometric

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[DrBarker]

This is really nice! I like how it essentially follows the classic algebraic proof too, so it could help people to the understand the algebraic proof at a deeper level, rather than being an "alternative" proof.

[PhilBoswell]

I think I'd have preferred to factor out the "a" in the final result, but maybe that's just personal taste…

[mushthaqazeez]

why not use x/a on one side and just go straight to x, x square and so on on the xaxis. wouldnt that be possible

[SomyaDwivedi-ji]

isnt x^2-x is wrong, it should be x^2-x-1. I dont get it