Alternating 1/4 Sum

This is a short, animated visual proof demonstrating the sum of the infinite geometric series with ratio -1/4.

And here is an alternating series dissection for powers of -1/3:

#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:

[noobhemingway]

Elegant, as usual! Always great to see your stuff while on Shorts.

[AlbinoJedi]

I'm surprised how much sense that made.

[bluecrystal_]

this is actually quite beautiful, never thought geometric math could make me genuinely smile :)

[bradnnn]

I learned the formula for this in pre-calc recently and solved this mentally in a few seconds; this is definitely a neat proof though

[hotdogskid]

Ah, i think i can see how this would generalize to -1/n now! I wonder if theres a neat way to do this without moving anything

[edwinthomasr]

I rem these from calc II. Love the visual representations! The thing that was so satisfying about them was figuring out if they went to infinity, negative infinity, or some constant!

[AnglandAlamehnaSwedish]

Dang so sweet ty for the video good one as usual

[voidsoul]

i remember doing this in school when I was bored
fun times, confusing times but fun times

[goatgamer]

It's 1/(X-1) for example 1/10+1/100+.. =1/9

[ai]

Geometrical interpretation is tough

With algebra ec


Take 1/a common

1/a*(a-a²+a³-a⁴....) =x
1/a(1-x) =x
1-x=ax
1=x+ax
X=1/(a+1)

[epicswordmewz]

Surely someone else must have thought that was the breaking bad logo at first glance...

[snaukball]

Isn't this the same as positives but just 1 minus that?
So the infinite sum of powers of negative 1/3 would be 3/4 because the infinite sum of positive 1/3 is 1/4 and you just do 1 minus that?

[averynemec-teup]

I have a question can you make things easy by like for example 1-1/2+(1/2^2)-… =2/3 but you can move the denominator to numerator and putting the new numerator which is 2 and +1 to that to get 3 as denominator so 2/3

[BitJams]

is there a way to write this in sigma notation

[PedraamJam]

if you dont add 1/4 ⁰(=1) then youll get -1/5 as the answer and not 4/5

[r.w.emersonii]

What could you prove if you used cubes instead of squares?

[musiquinhasdaoras]

Ok, but how to visualize this demonstration using just one square, is it possible?

[Tletna]

It looks like 4/9ths of the 9 square grid. I'm confused on how it is 4/5ths. I'm missing something crucial here, I guess.

[Holobrine]

This proof works for all bases:
x =
10x =
10x - x = 1
(10 - 1)x = 1
x = 1/(10 - 1)

[marianne-wtit]

Can someone help me on how can I improve my geometrical interpretation it's very poor