The video owner has disabled playback on external websites.
This video is no longer available on YouTube.
This video cannot be played right now.
Watch on YouTube
ابزارهای یادگیری هوش مصنوعی را باز کنید
ثبتنام کنید تا به ابزارهای قدرتمندی دسترسی پیدا کنید که به شما کمک میکنند سریعتر از هر ویدیو یاد بگیرید.
ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12
آمار یادگیری
سطح CEFR
سختی
زیرنویسها (136 بخشها)
I'm gonna give you an astounding result
Astounding?
An astounding result
So I'm just gonna write down a little sum
I'm just gonna see what answer it gives.
1 + 2 + 3 + 4 + duh duh duh duh duh
And I include all the natural numbers, so all the way up to infinity
So what do you reckon the answer to this is, Brady?
-Well I would say it would go to tend towards infinity.
Yeah, that makes sense, doesn't it.
The answer to this sum is -- remarkably -- minus a twelfth.
It's amazing! I mean, I first saw this result when I start learning a bit of String Theory
And what's even more bizarre is that this result is used in many areas of physics
This is a very well known string theory textbook by Joe Polchinski. As you can see,
sort of quite early on, page 22, we have this statement here which is that the sum of
all this is --- basically saying the sum of all the integers ---
all natural numbers all the way up to infinity, is, minus a twelfth.
Alright so we're going to prove now,
Without getting our knickers in a twist with Riemann zeta functions, we gonna prove
in quite simple way, why the sum of all the natural numbers is indeed minus a twelfth.
So, to do that we're gonna do this in a number of steps.
We're gonna to look at a few different sums.
The first sum that I want to look at, I'm gonna call it S1.
And it's 1 -1 +1 -1 +1 -1 and so on.
That's the first sum I wanna look at in principle.
The second sum I'm gonna look at is 1-2+3-4 and so on
Carry on in that process all the way up.
And the third one is of course going to be
زیرنویس کامل در پخشکننده ویدیو موجود است
با تمرینها یاد بگیرید
تمرینهای واژگان، گرامر و درک مطلب از این ویدیو بسازید
نظرات (0)
برای نظر دادن وارد شویدثبتنام کن و همه امکانات رو باز کن
پیشرفتت رو دنبال کن، واژگان رو ذخیره کن و تمرین کن
حالت تعاملی
آزمون
پاسخ صحیح:
ویدیوهای مرتبط
WATCH | Knife-wielding man shot after attacking cops, motorists on Joburg road
Math Magic
Why You Will Marry the Wrong Person | Alain de Botton | Google Zeitgeist
My Octopus Teacher, My Sh*t Son (My Octopus Teacher parody)
Scotland’s West Highland Way: A Journey Into the Highlands
Numberphile
آزمون
پاسخ صحیح:
آزمونها هنگام تماشای ویدیو ظاهر میشوند
راهنمای حفظ
از این ویدیو
شروع رایگان یادگیری زبان
