Sum Geometric Series with Ratio 1/2 in Rectangles (visual proofs)
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: • Geometric Sums
This animation is based on a proof by Ángel Plaza in the June 2024 issue of Mathematics Magazine (https://doi.org/10.1080/0025570X.2024... page 328).
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries #rectangle #silverratio #goldenratio
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