Infinite Series - Numberphile

The real reason Achilles can never reach the tortoise is because it turned around, bit him in the ankle, and Achilles died.

I noticed that infinite numbers graph finite shapes and finite numbers graph infinite series.

What about 1/3+1/9+1/27+1/81... and 1/9+1/81+1/729+1/6561...?

Well this man kinda looks like Qassim Soleimani 😅

I'm so tired of pi. This video is about plain old infinite series, so I should be safe.

in which category you place infinity number theort

Someone should have told the Mayans about the harmonic series to help them improve on their Corbel arches and vaults.

This is great, I'm learning about these I my Cal II class, and this just deepens my understanding of the infinite sums and series

I love the way he handled the infinity question !

The second series grows super slowly by the time you get to 1/1,000,000 you'll have only got to 14.39

animation is a blast!

This is the weirdest Burke’s Backyard crossover ever.

So non linear linear and surface linear. Time mergers. Surfaces are curvatues of harmonics. Frequency squares damping.

If you are interested to learn more about divergent series and want to understand why and how 1+2+3+4+5+6+... = -1/12,
I recommend the online course “Introduction to Divergent Series of Integers” on the Thinkific online learning platform.

That's one reason pi is the coolest number :-)

Every time it starts beeping I think "Super Mario World".

Very smooth and lovely

im here from jujustu kaisens manga

So, according to the harmonic series (1+1/2+1/3+....),Zeno was indeed right...

The pile of cards with harmonic series is depicted in a math book. I've been searching for that book since a few years. I downloaded and read some part of it back in 2017. I lost it somehow and now I don't remember the name of the book. Is there anyone who knows the name of that book? Thanks!

Pi popping up somewhere is more annoying than a Rick Roll.

Infinite Series Bla Bla which Never Ends.

Pacek is:
1 ÷2
All over 12
time if you dubll 1 or 2 you will not reach the end it's infinity

Where's the famous "brown paper"?😕

Pujara ??

Summing squares of 1/x where x increments each squared value is well-known to have a relationship with pi, though.

Gazillion really

This guy looks like Bob Mortimer 2

Zeno, messing with people's heads for millennia

jujutsu kaisen that is all

If we’re just going by a divergent or convergent series, why is the sum of 1+2+3+4+5… = -1/12 not mentioned even though it is divergent?

Jujutsu kaisen brought me here

What about the most important sum:
Sum 41?

1 + (½)² + (⅓)² + ...... = π²/6. How.??

So, you want to have lots of annals? Become a mathematician.

You've made Math fun. Thank you. <3

infinity is possibility (in - finity) in something, between something - there are possibilities to definition
(expression) space for existence - defined

Roberto De Niro ???

Pulsating text animation is make from 4 frames

Thank you

And just like that, it ends.

Pi creeps in where you least expect it. Right, like this video.

1 + 1/2 + 1/4 + 1/8…

Every possible number in this series has the same two properties in common: A. It diminishes the ‘gap’ (between the accumulating number and 2). B. It fails to close the gap between the accumulating number “2”.

Since every possible number in the whole series is incapable of closing the gap it diminishes, adding all of the numbers (the ‘infinite sum’) does not involve adding any number which reaches 2. Achilles does not catch the Tortoise.

Also, since the gap size (the distance between the accumulated number and 2) is the last number in the series (gap of 1/4 at 1+1/2+1/4) the accumulation of numbers can never result in the closure of the gap.

The 1st infinite series mentioned corresponds to a different Zeno's paradox - that of dichotomy paradox.

APRIL 30 2024 THERE ARE 593 ANNALS OF MATHEMATICS

I wonder. How far on the x axies will "volume 1" move for the Grahams Number of terms?

You forgot to mention that the tortoise is always moving forward. Paradox

You forgot to mention that the tortoise is also always moving forward. Like Achilles is. You didn't solve the Zeno's paradox. That's why civilization will go on remembering Zeno and not you.

thank you for this great video

How come the sum of first 50 trillion terms in harmonic series is more than 50 trillion?