Alternating Geometric Series (visual proof)

Рет қаралды 5,113

Жыл бұрын

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This is a short, animated visual proof demonstrating the infinite alternating 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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Also, check out my playlist on geometric sums/series: • Geometric Sums
This animation is based on a proof by The Viewpoints 2000 group from the October 2001 issue of Mathematics Magazine page 320 (www.jstor.org/stable/2691106 ).
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Пікірлер: 20

@Dillbeet Жыл бұрын

Beautiful. I love how even and odd increments are adjacent each other

@MathVisualProofs Жыл бұрын

Thanks!

@user-fr2jr6hd4i Жыл бұрын

if possible, please make animation like this to explain the series expansion of ln, e^x, sin, cos, tan ,sinh, cosh

@Lucashallal Жыл бұрын

kzfaq.info/get/bejne/rpZpfNaTu8DJiKM.html Here for sin

@agrajyadav2951 Жыл бұрын

Epic 🤘

@MathVisualProofs Жыл бұрын

😀

@anatolykarpov2956 Жыл бұрын

Very elegant ❤

@MathVisualProofs Жыл бұрын

Thank you! 😊

@mehulpunia6174 Жыл бұрын

Let S be the set of all 5 digit numbers formed using the digits 1,2,3,4,5 without repetition. find the sum of all the numbers in S.

@anarchosnowflakist786 Жыл бұрын

I imagine the result could look like (11,111+22,222+...+55,555)*x=15*11,111*x=166,665*x ? and since each digit will appear in each position a number of times equal to the number of combinations (without repetitions, so an enumeration) of the 4 other digit in the 4 other positions of the number. x is therefore easy to calculate, it's 4*3*2*1=24 this would give us a result of 3,999,960 am I close ? edit : also you successfully just nerd sniped me

@joserios4359 Жыл бұрын

Me facina estas demostraciones visuales

@MathVisualProofs Жыл бұрын

Glad you enjoy them!

@yassinebelhaj5447 Жыл бұрын

this vid is amazing

@MathVisualProofs Жыл бұрын

Glad you liked it! 😀👍

@davidgonzalez2844 Жыл бұрын

Amazing!!! I have needed this type proof when I student Math! Thanks for your video

@MathVisualProofs Жыл бұрын

Glad it was helpful!

@dishangdoshi9966 Жыл бұрын

sir how did you got ar, ar^2 as the lengths? I saw your video of series x>0 but here i am not getting it. I Tried by dist formula but aint getting the result

@MathVisualProofs Жыл бұрын

For ar, we plug x=a into y=a so the top y coordinate is a, and we plug x=a into the line y=-rx+a so we get bottom y-coordinate of -ra + a. When I subtract these two y-coordinates to get the length of the vertical yellow line, I get a-(-ar+a) = ar.

@FrumiousBandersnatch42 Жыл бұрын

I tried to recreate this sum in Desmos, and it seems that as r reaches 1, this becomes incorrect.

@MathVisualProofs Жыл бұрын

This won't work for r=1 for sure. It should work for any number less than r, but there is always a chance that the tolerance or round off error in Desmos will cause a problem.