Geometric Series: Alternating Sum of Powers of 1/4 (visual proof)

This is a short, animated (wordless) visual proof demonstrating the sum of the infinite geometric series with ratio -1/4. #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #geometricseries #infiniteseries #fractals #sum #induction #mathshorts​ #mathvideo​

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

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Creative Commons Attribution-ShareAlike 3.0 Unported

[Mutual_Information]

Wordless visual proofs are really satisfying. Well done as always

[mathflipped]

I wondered what the second square is for. Nice trick!

[Bunnokazooie]

A little tricky, took me a few times (and reading the comments) to fully understand it. I wonder what the proof would look like if the two portions were labeled separately.

[TARIKÖZDEMİR]

In first picture There are two pictures 1+1/4 i dont understand this