Abel Sum of Grandi’s Series @MathVisualProofs

Uploaded May 2026 | Updated September 2026, 2 weeks ago

Abel Sum of Grandi’s Series

We show how an amazing visual proof of the infinite alternating geometric series formula for any positive ratio r with r less than 1 allows us to make sense of one particular Abel sum assignment of a value to a famous divergent series.

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To see the original alternating series proof short, check out :
youtube.com/shorts/ttSl8bMmwKA?feature=share

For a slower, wide format version of the alternating series proof (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 ).

#math #calculus #manim #abelsum #divergentseries

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