Infinite Geometric Series Sum Formula III (visual proof)

Thanks!

This is a short, animated visual proof demonstrating the infinite geometric series formula for any positive ratio r with r less than 1 and with positive first term a. This series is important for many results in calculus, discrete mathematics, and combinatorics. #mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries

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Music in this video:
Pangelic
The Mini Vandals

[lgooch]

Wow I’ve never seen this proof, but this might be my favorite geometric one. Great vid!

[purplenanite]

It's cool how this also makes some sense for r outside the range from 0<r<1!

[josecarloslozanopacheco]

It reminds me about the new proof of Pythagoras Theorem. Anyway, your proofs are always great 😉😉

[pengin]

What would also be nice to see are videos about graph theory! I think there are nice visual proofs for Eulers polyhedron formula, have you ever considered doing something like that?

[TheJoyLoveShow]

Thank you for your great work!! How specifically did you decide to derive (a/(1-r))? Thank you.

[MyNordlys]

About the short "An random approximation for Pi" where we cant comment and discuss, we have pi²/6 = Total/Red but also equals Zeta(2)... Is it an another bridge between Zeta and prime numbers ?

[Yusuf-cgzt]

Could you do one for trigs functions on a plane, the longer i gaze into their shapes the more i get confiused, especially dervitives, integrals and identities of trigs functions

[vennstudios]

for a second I thought you were gonna make it into a summation