Infinite Sum of Powers of -1/7 in a Square (visual proof without words)

This is a short, animated (wordless) visual proof demonstrating the sum of the infinite geometric series with ratio -1/7.

And here is an alternating series dissection for powers of -1/3:

And here is an alternating series dissection for powers of -1/4:

#math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #geometricseries #infiniteseries #fractals #sum #induction #mathshorts​ #mathvideo​

To learn more about animating with manim, check out:
_______________________________
Music in this video:
Creative Commons / Attribution 3.0 Unported License (CC BY 3.0)

[jasonrubik]

This is great. I feel that an opportunity was missed at the beginning to more clearly visualize why the triangular quadrant plus one small square was equal to 1/7. The runtime requirements for this exposé could have been offset by a reduction in the number of subsequent iterations, as they seemed to be a tad bit redundant. Otherwise totally awesome proof. I've never seen this limit before

[daniel_.]

omg I remember that literally 1 year ago you just had 12k subs. now you have 10x ❤