This is a short, animated visual proof showing the sum of the infinite geometric series with first term 6/7 and ratio 1/7, which in turn allows us to compute the sum of the series of powers of 1/7 and determine an interesting base 7 representation of 1.
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For a longer, wordless version of this animation with two other proofs, see • Three Geometric Series in an Equilate...
Also, check out my playlist on geometric sums/series: • Geometric Sums
This animation is based on a proof by Stephan Berendonk (2020) from the November 2020 issue of The College Mathematics Journal, (https://doi.org/10.1080/07468342.2020... p. 385)
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Watch video 0.66666… = 1 (in base 7) online without registration, duration hours minute second in high quality. This video was added by user Mathematical Visual Proofs 17 June 2024, don't forget to share it with your friends and acquaintances, it has been viewed on our site 387,805 once and liked it 25 thousand people.