Sum Geometric Series with Ratio 1/2 in Rectangles (visual proofs) @MathVisualProofs

Uploaded June 2024 | Updated September 2026, 2 weeks ago

In this video, we show an animated version of a recent proof without words that finds the sum of the geometric series with first term 1/root(2)+1/2 and ratio 1/2 using the unit square. Then we show how to find other geometric series sums with ratio 1/2 using different sizes of rectangles. Careful, the final bonus question might require a different technique than rotating :)

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

This animation is based on a proof by Ángel Plaza in the June 2024 issue of Mathematics Magazine (doi.org/10.1080/0025570X.2024.2336443 page 328).

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Sum Geometric Series with Ratio 1/2 in Rectangles (visual proofs)

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