Geometric series: sum of Powers of 1/7 (visual proof)

This is a short, animated visual proof demonstrating the infinite sum of the powers of 1/7. #mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #geometricseries #series #infinitesums #infiniteseries

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[alvarol.martinez]

Nice, perhaps this could have lasted 30 seconds tho (just hoping more people engage with your content)

[DrBarker]

You have some great visual proofs for geometric series! I wonder if there is a visual proof for every geometric series with rational common ratio, e.g. could you do 3/11 + (3/11)^2 + (3/11)^3 + ..., or would you need it to be a "nice" series in some sense?

[jimboli]

Does this work for other powers with n segments. i.e does the sum of 1/n powers tend towards 1/(n-1)?

[NumbToons]

Can you tell me one thing. Are all geometrical series representable by some geometrical objects?

[saikatkarmakar]

More generally through the same way we can prove that "1/n+1/n²+1/n³+1/n⁴+... =1/(n-1) for n>1".

[AbhijnanGogoi]

Wow! Awesome animation! Did you use Manim? The animation style seems similar to it.

[shubhamg]

Make a video about divisibility rule of 7.

[theoverseer]

Does this apply to all whole-number fractions?

[scmtuk]

So, basically, the sum of the powers of 1/n = 1/(n-1)?

So, that means the sum of the powers of 2, would mean that, since 2 = 1 / (1/2), then the sum would be 1 / (1/2 - 1) = -1 / 1/2 = -2
The sum of the powers of 3 would be 1/(1/3 - 1) = -1 / (2/3) = -3/2?

[Wafflical]

You could also prove this using the Gosper island, couldn't you?