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Curated by: Mathematical Visual Proofs (650 videos)
If you like this content, consider joining my Patreon (free or paid memberships): https://www.patreon.com/c/MathVisualProofs In this video, we show James Tanton's dissection proofs for infinite geometric series of of the sum of positive powers of 1/(n+1). The sum is 1/n, and the proof uses a clever dissection of a regular n-gon. We show the visual simultaneously for regular n-gons for n=3 to 10, but the same argument works for any integer n greater than 2. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! For other compilations of geometric series dissections see: https://youtu.be/JteQEN1XPyc or https://youtu.be/gN4EFwF5Hro For a more general result see https://youtu.be/V7L5nsRj7CE or https://youtu.be/Qa0bOHYjnW0 This animation is based on a proof by James Tanton from the March 2008 issue of The College Mathematics Journal page 106. (https://www.jstor.org/stable/27646594). #manim #math #mathvideo #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #calculus #series #geometricseries #infiniteseries #dissection #dissectionproof #geometricsum #sums #calculus2 To learn more about animating with manim, check out: https://manim.community