This is a short, animated visual proof showing the sum of the infinite geometric series with first term 8/9 and ratio 1/9, which in turn allows us to compute the sum of the series of powers of 1/9 and determine an interesting base 9 representation of 1.
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For a longer, wordless version (more dramatic) of this animation see
• Geometric series: sum of powers of 1/...
Also, check out my playlist on geometric sums/series: • Geometric Sums
This animation is inspired by the a proof by Elizabeth M. Markham from the October 1993 issue of Mathematics Magazine page 242 (https://doi.org/10.2307/2690738).
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Watch video 0.8888… = 1 (in base 9) online without registration, duration hours minute second in high quality. This video was added by user Mathematical Visual Proofs 08 August 2024, don't forget to share it with your friends and acquaintances, it has been viewed on our site 21,848 once and liked it 1.4 thousand people.