Differentiated Geometric Series without Words @MathVisualProofs

Uploaded March 2025 | Updated September 2026, 2 weeks ago

This is a short, animated visual proof computing the sum of a differentiated geometric series with ratio given by positive real number x less than 1. The proof uses a dissection proof of a 1/(1-x) by 1/(1-x) square using the formula for the infinite geometric series with ratio x.

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This animation is based on a visual proof by Roger B. Nelsen from the September 2001 issue of The College Mathematics Journal (jstor.org/stable/2687557 p. 257).

For related videos, see:
youtu.be/2d4CTG1uJs8
youtu.be/2WuSNveg-1c

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