Uploaded May 2026 | Updated September 2026, 2 weeks ago

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Summing Powers of 8 via Self-Similarity

This is a short, animated visual proof demonstrating the finite geometric sum formula for any integer n with n greater than 3 (explicitly showing the case n=9 with k=3). This series (and its infinite analog when x less than 1) is important for many results in calculus, discrete mathematics, and combinatorics.

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For a longer version of this video with other geometric sums (to see how this generalizes), check out: youtu.be/1wIdJxSfUz4

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

This animation is based on a proof by Mingjang Chen from the December 2004 issue of Mathematics Magazine page 373 (doi.org/10.2307/3219202).

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