Adding powers of 1/2

This is a short, animated visual proof demonstrating the infinite sum of the powers of 1/2 using an isosceles triangle. #mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #geometricseries #series #infinitesums #infiniteseries

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[ScenicFlyer]

Half it and give it to the next person

[mathman]

New approach, it was normally done by a square but you tried new that is amazing

[carultch]

An infinite number of mathematicians walk in to a bar. First orders a pint, the next orders a half pint, followed by a quarter pint order, and so forth. All of the same kind of beer.

The bartender serves them two pints, and says, "you guys don't know your limits, do you?"

[ritorapid]

my Life is now complete following these shorts from 1/8 hehe

[AkariLimano]

Thanks, I love your geometric interpretations. I am a visual person and infinite series drove me nuts in university. Now I can see the beauty behind those formulas

[jackstonebaby]

I love these geographic representations of infinite sums.

[Sloop_Jonz_B]

These videos are great. I’m a project cost estimator who was never allowed to take difficult math courses in school (they didn’t believe someone with autism can do math I guess). Now I’m in my late 20s and math is easier than I ever imagined. Thank you for helping me change my life for the better.

[fire]

So sum of 1/N^k = 1/(N-1)
Seems consistent across your videos

[p.g.]

Some comments here say it is actually=1.

That is actually not true. By giving the infinite sum a number = x, you are already made the assumption that is in a fact a finite number. It is not. It is converging to 1.

The math behind that is not complicated, it is the geometric sequence. In fact, here it is s= (1-q^(n+1)/ 1-q) - 1
In this case q = 1/2 and n would be infinity.

So you have to find the lim of this function. For any q < 1, q^(n+1) will always converge to 0. But this will ultimately cause that you cannot use the equal sign. You have to use ➡️

[SteveMathematician-thco]

This can be solved just by Geometric progression formula, but this is better to understand it

[AngryEgg]

Here is the mathematical solution very simple:

a1 = 1/2
q = 1/2
Sum of an infinite geometric sequence:
a1/(1-q) => (1/2)/(1-(1/2)) = (1/2)/(1/2) = 1

[anjalidwivedi]

the actual answer is that the sum will keep on approaching 1 but will never reach 1....but for explaining this will work too👍👍

[z]

Terrance Howard made VR and new tech drones with this knowledge 😊

[dvargart]

My brain is ripped apart between choosing to believe this lol

[Xbrh]

One must imagine the isosceles triangle happy...

[sumitsarmah]

This can be also done with the help of a Square

[cipherxen]

Now he'll do the same series with all other shapes

[sumdumbmick]

no, you never reach the corner point. so it's 1 -L(0), where L(0) is the inverse of positive infinity, and the point adjacent to 0 on the numberline such that lim x->0+ 1/x = 1/L(0)

[DrRiq]

I prefer the square tbh. The triangle looks like half a square the way it's placed

[eastonbrunet]

MISTAKE
1/1024 is actually the answer, not 1/1028.