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Summing Arithmetic Sequences Visually (proof without words)

This is a short, animated visual proof demonstrating how to visualize the sum of an arithmetic sequence, producing a closed formula for such a sum. This is visual is based on proofs known to the ancient Greeks and can be found in Roger B. Nelsen's book Icons of Mathematics (page 177): https://bookstore.ams.org/dol-45 Specializing to a = 0 and d = 1 gives the sum of the first n integers (triangular numbers) formula. Specializing to a = 1 and d = 2 gives the sum of the odd integers (which yields the squares). In general, we can get any polygonal number formula from this fact (in addition to many others). If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualPr.... Thanks! #mathshorts​ #mathvideo​ #math​ #numbertheory #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #squares #triangularnumbers #arithmeticsum #arithmeticsequence #finitesums To learn more about animating with manim, check out: https://manim.community _________________________ Music in this video: Prelude 2 by VGM Mark H |   / user-656562764   Music promoted by https://www.free-stock-music.com Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/...