Two Geometric Series in an Isosceles Trapezoid (visual proof without words)
This is a short, animated visual proof demonstrating the sum of two infinite geometric series using dissection proofs in an isosceles trapezoid. In particular, we show how to find the sum of powers of 1/4 and the alternating sum of powers of 1/2 using the isosceles trapezoid. Geometric series are important for many results in calculus, discrete mathematics, and combinatorics.
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Also, check out my playlist on geometric sums/series: • Geometric Sums
This animation is based on a proof by Roger B. Nelsen in his book Cameos for Calculus (https://bookstore.ams.org/clrm-49/ ).
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Music in this video:
Traveling Around The World by Alex-Productions | https://onsound.eu/
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Creative Commons / Attribution 3.0 Unported License (CC BY 3.0)
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