Alternating Geometric Series Sum @MathVisualProofs

Uploaded June 2024 | Updated September 2026, 2 weeks ago

This is a short, animated visual proof demonstrating the infinite alternating geometric series formula for any positive ratio r with r less than 1 and with positive first term a. This series is important for many results in calculus, discrete mathematics, and combinatorics.
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For a slower, wide format version of this video (without words), see youtu.be/Qa0bOHYjnW0

Also, check out my playlist on geometric sums/series: youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw

This animation is based on a proof by The Viewpoints 2000 group from the October 2001 issue of Mathematics Magazine page 320 (jstor.org/stable/2691106 ).

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Visualizing the Digits of e | 1000 Digits of Euler’s Number