This is a short, animated visual proof computing the sums of the series of reciprocals of specific binomial coefficients, namely those obtained by considering one column in Pascal's triangle. Amazingly, the same geometric argument, relying on telescoping, will give a nice formula for the infinite sum of reciprocals of each column.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualProofs. Thanks!
For a related video showing just one column, see this video:
• Infinite series: summing reciprocals ...
This animation is based on a visual proof by Tom Edgar from the June 2016 issue of Mathematics Magazine (www.jstor.org/stable/10.4169/math.mag.89.3.212 page 212-213 ).
#mathshorts #mathvideo #math #infiniteseries #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #calculus #triangularnumbers #animation #theorem #proof #iteachmath #series #infinitesums #infiniteseries #pascaltriangle #binomialcoefficients #binomials #binomialtheorem #telescoping
To learn more about animating with manim, check out:
manim.community/
Mathematical Visual Proofs