Infinite Geometric Series Sum

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.

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[МаксимАндреев-щб]

This picture is like the picture for the trigonometric proof of Pythagorean theorem

[Hamza_Khan_Journey]

Very neat perspective on the converging geometric series

[US-ywxi]

As the video proceeded, I saw myself learning something new and actually useful.
Thank you!

[Drz.]

Thats brilliant. Keep making cool videos like these mate

[raymitchell]

Neat proof, I'm trying to recall long ago how we handled converging series... and once again those isosceles triangles are so underrated

[pelayomedina]

There is a small detail, the lines only intersect if r<1, so the sum is not valid if r>=1

[SkalopSkalop-xomj]

The beauty of the geometric series that you can demonstrated its sum with cool way like this besides the analytic way, and your explanation is good, great video

[Phylaetra]

This is a brilliant visual proof! Thank you!

[mcalkis]

What a beautiful proof. Thank you for making this.

[andrewmartin]

i love this proof, it’s so easy to derive i literally never will learn the formula except temporarily

[jaidenminott]

doing this right now in calc 2. this is actually really helpful

[Ninja]

Its interesting that this proof also shows why we need r<1 because if r>1, the lines would get further apart and never interesct.

However, I wonder if there is a variation of this proof that could get work for negative r values. That would be very interesting

[cayoford]

really cool proof, and I love the way you explained it, minus it going by a bit fast and me needing to pause a couple times to take it in

[nilsalmgren]

Try doing the algebra starting with x= rx+a and solve for x. x-rx = a. x(1-r) = a. x = a/(1-r)

[aboobakarmohammed]

Ok now I won't forget that formula again❤

[p_dadon]

I was just working on geometric sequences form AMC 10 yesterday, and derived a/(1-r). This is a neat proof

[afrika-karibianaestudionan]

Thanks for this video. It is very useful when introducing the concept of limits.

[sniperk]

Interesting geometric way to compute powers of r

[SeanSkyhawk]

I almost thought this was the new proof I've been waiting for :(

[TheOriginalDeaf]

This looks like the same triangle for proving Pythagorean theorem using trigonometric functions, everything in math is related in some way or another ❤