Geometric series: sums of powers of 9 are Triangular (visual proof)

This is a short, animated visual proof demonstrating how to visualize the sum of the finite geometric series of powers of 9 by showing that such a sum is a triangular number. #mathshorts​ #mathvideo​ #math​ #numbertheory #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #series #triangularnumbers #geometricsum #geometricseries #finitesums #discretemath

This animation is based on a proofs by Roger B. Nelsen from the October 1990 issue of Mathematics Magazine page 225 (https://doi.org/10.2307/2690939 ).

To learn more about animating with manim, check out:
https://manim.community

Music is Rulers of our Lands by Rafael Krux (https://freepd.com/).

Видео Geometric series: sums of powers of 9 are Triangular (visual proof) канала Mathematical Visual Proofs