0.66666… = 1 (in base 7)
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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