Exploring the Geometry of Infinite Geometric Series: 8 Visual Proofs

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: https://youtu.be/saJJGNlsfn8 (attribution: Roger B. Nelsen)
r = 1/3: https://youtu.be/RmTZmNrkqss (attribution: Rick Mabry)
r = 1/4: https://youtu.be/8i1xj5ORwUw (attribution: Rick Mabry)
r = 1/5: https://youtu.be/IguRXWNwrn8 (attribution: Rick Mabry)
r = 1/6: https://youtu.be/o0AyHmRV8RA (attribution: James Tanton)
r = 1/7: https://youtu.be/6wgCoIzsaA8 (attribution: James Tanton)
r = 1/8: https://youtu.be/wPgwgoj_aKA (attribution: Roger B. Nelsen)
r = 1/9: https://youtu.be/nQb11RIEXkI

If you like series dissections, check out my playlists:
https://youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw
https://youtube.com/playlist?list=PLZh9gzIvXQUv6JqhlqQDlnqQw1NczW5Ro

#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 | https://soundcloud.com/scottbuckley
Music promoted by https://www.free-stock-music.com
Attribution 4.0 International (CC BY 4.0)
https://creativecommons.org/licenses/by/4.0/