Beautiful Geometry behind Geometric Series (8 dissection visual proofs without words)

This video is a compilation of eight shorter videos I have created showing dissection proofs for infinite geometric series with ratio of the form 1/n and first term 1/n. To see the original videos (in shorter form and typically with more dramatic music), check the links below. When you have seen enough of these dissections, you should be able to guess the general formula for such a geometric series (and perhaps the more general form, which can be found in other videos on my channel).

Here are the original series videos (along with attribution; for more detailed attribution, see the original videos):

r = 1/2:    • Geometric series: sum of powers of 1/2 (vi...   (attribution: Roger B. Nelsen)
r = 1/3:    • Geometric series: sum of powers of 1/3 II ...   (attribution: Rick Mabry)
r = 1/4:    • Geometric series: sum of powers of 1/4 (vi...   (attribution: Rick Mabry)
r = 1/5:    • Geometric series: sum of powers of 1/5 II ...   (attribution: Rick Mabry)
r = 1/6:    • Geometric Series: sum of powers of 1/6 (vi...   (attribution: James Tanton)
r = 1/7:    • Geometric series: sum of Powers of 1/7 (vi...   (attribution: James Tanton)
r = 1/8:    • Geometric Series: sum of powers of 1/8 (vi...   (attribution: Roger B. Nelsen)
r = 1/9:    • Geometric Series: sum of powers of 1/9 (vi...  

If you like series dissections, check out my playlists:
   • Geometric Sums  
   • Infinite Series  

#manim #math​​ #mathshorts​ #mathvideo​ #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #calculus #series #geometricseries #infiniteseries #dissection #dissectionproof #geometricsum #sums #calculus2

To learn more about animating with manim, check out:
https://manim.community
___________________________________
Music:
Adrift Among Infinite Stars by Scott Buckley |   / scottbuckley  
Music promoted by https://www.free-stock-music.com
Attribution 4.0 International (CC BY 4.0)
https://creativecommons.org/licenses/...