Summing powers of 1/8 visually!

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:    • Geometric Series: sum of powers of 1/...  

Here is a longer form video with lots of related infinite geometric sums:    • Beautiful Geometry behind Geometric S...  

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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).

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