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.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualPr.... Thanks!
Here are two alternating series dissections for powers of -1/2: • Alternating Geometric ...
• Alternating Geometric ...
And here is an alternating series dissection for powers of -1/3:
• Alternating Geometric ...
And here is an alternating series dissection for powers of -1/4:
• Geometric Series: Alte...
#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:
manim.community
_______________________________
Music in this video:
Doing My Best by Alex-Productions | onsound.eu/
Music promoted by www.free-stock-music.com
Creative Commons / Attribution 3.0 Unported License (CC BY 3.0)
creativecommons.org/licenses/...

[@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

[@MathVisualProofs]

Thanks! I hear your suggestion for sure. I figured since each iteration shows the same dissection that one might eventually see the 1/7 by counting. Or they could pause. But I probably could have done something at the beginning to make the 1/7 more clear. Still practicing 😀

[@jasonrubik]

@@MathVisualProofs practice makes perfect !! 🥳

[@Fire_Axus]

your feelings are irrational

[@marciorjusto]

Fantastic!!! 👏🏾👏🏾👏🏾

[@ruilopes00]

Beautiful

[@MathVisualProofs]

Thank you

[@daniel_77.]

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

[@MathVisualProofs]

Thanks for sticking around. Growth is fast sometimes :)

[@David-bh7hs]

@@MathVisualProofs I can’t wait until 6 years from now when every human being alive will be subscribed to this channel.

[@Gunslinger-us1ek]

@@MathVisualProofs growth rly said e^x 😂

[@MathVisualProofs]

@@David-bh7hs Hah!

[@user-cx4uf8gw7v]

super!

[@MathVisualProofs]

Thanks!

[@FlayGD-ol7lz]

Awesome

[@MathVisualProofs]

Thanks!