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This is a short, animated visual proof showing the sum of the infinite geometric series of powers of 1/8 (starting with 1/8) is 1/7 using self similar trapezoids in a regular heptagon. #manim #math #mathshorts #mathvideo #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #calculus #series #geometricseries #infiniteseries #heptagon #trapezoids Here is an alternate dissection proof for this series: Here is a longer form video with lots of related infinite geometric sums: If you like this video, consider subscribing to the channel or consider buying me a coffee: Thanks! This animation is based on a proof by James Tanton from the March 2008 issue of The College Mathematics Journal page 106. (). To learn more about animating with manim, check out:
