why does 1+1/2+1/3+... = infinity?

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[ErtosAcc]

Very clean proof. Basically relies on the fact that if something is bigger than infinity, then it must be infinity. Really nice.

[violintegral]

By the way, it was Nicole Oremse who first used this comparison to show the divergence of the harmonic series. As a sidenote, I think this simple proof of the divergence of the harmonic series would be great to introduce the comparison test to a Calculus 2 class.

[fuscello]

I haven’t even studied series + the semi language barrier (I’m Italian, so I don’t understand every single mathematical term), but still you make these videos clear and fun to watch

[BenzilJohn_infinity]

Legends say that he's still holding that pokeball.

[logistaur]

Man this was such a nice video, a good memeoy refreshment
And you can tell that you are very excited about it/sharing your knowledge in a simple way.
You would make a great math teacher

[Scryllix]

This is the first video I've seen from you an d i already know I'll be watching more! That was really interesting

[Ninja]

very useful. I also watched eddie woo and khan academy doing the same proof, but i feel yours was the most helpful as it shows why u choose the powers of 2 for the denominator

[RaceCmart]

Let's just appriciate the pokemon thingy in his hand, he was holding it for entire video. Great power. Infinity out of infinity

[gustafbstrom]

Thanks, love your pedagogy. Keep up the good work!

[sergioh]

Wasn't aware of this classic proof! But so far I love it! Beautiful

[yelnatspowerzz]

From 2:45 to 5:45 makes the most sense. Example u will eventually get to 1/8 which is .125 by the time u add up all of the numbers before 1/8 u will get a number of .5 or greater which means by the time u hit 1/8 u get +.5 then same when u hit 1/16 u will have another .5 by then, yet again with 1/32 another .5 essentially always giving you +.5+.5+.5 eventually getting you to infinity

[muzankibutsuji]

we can use ln(1+x) expansion
ln(1+x)=x-x^2/2+x^3/3-x^4/4
ln(1-x)=-(x+x^2/2+x^3/3....)
putting x=1
ln0=-(1+1/2...)
-infinity=-(1+1/2...)

[antro_phagus]

I stumbled upon this video by mere chance, as I never watch math related content

I was pretty much expecting not to understand anything... but, I was able to follow along for the entire video, and it really turned out to be very interesting! Your explanation is amazing, and it genuinely made me enjoy math even if I'm rarely good at it

Thanks so much for sharing! This is a very cool video <3

[JulianShagworthy]

Imagine you walk 10 metres, but split it into sections, the first section being 5 metres, then every subsequent section being 1/4 the length of the previous one. No matter how many times you apply this, you'd never reach 10 metres. But you do. So you've surpassed an infinite number of sections by walking ten metres :)

[mikejackson]

I love your videos Steve! Keep up the good work mate! 👍👍👍

[SmokeyMagma]

Very good video, especially now with calculus 2 in the spring semester!

[dimasveliz]

I knew about the sum of inverted powers of two being equal to two, but this divergent sum proof using the prior one was astonishing! Awesome video

[sergioh]

Hi Steve, just found this other channel. Just subbed as well. I'm looking forward to watching you again! And all throughout the year. Keep up the good work! So far I'm liking this video and this is my first one I'm watching on this channel 😊

[danielevilone]

I would simply notice that the sum S = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +... if we assume it finite must be strictly larger than the sum S' = 1/2 + 1/2 + 1/4 + 1/4 + 1/6 + 1/6 +... (where we substituted each odd terms with the next one): S > S'. But it is easy also to see that S' = S ==> contradiction.

[ImaginaryHuman]

makes sense on paper, still strange to think that you can add infinitely many numbers that keep getting smaller and it diverges