This is a short, animated visual proof demonstrating the infinite sum of the powers of 1/4.
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Thanks!
To see two other versions of this sum, check out
• Geometric series: sum of powers of 1/...
• A Hexagonal Geometric Sum (visual pro...
To see the related base 10 fact, check out:
• 0.999999… = 1
And to see the related binary fact, check out:
• Adding powers of 1/2
To see related base-3 fact, check out:
• Geometric series: sum of powers of 1/...
or
• 0.2222…= 1 (in base 3)
To see a related base-5 fact, check out
• 0.4444... = 1 (in base 5)
This animation is based on a proof by Sunday A. Ajose from the June 1994 issue of Mathematics Magazine (https://www.jstor.org/stable/2690616 page 230).
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To learn more about animating with manim, check out:
https://manim.community
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