0.8888… = 1 (in base 9)
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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To learn more about animating with manim, check out:
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