/sci/ - Science & Math » Thread #13985716

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Anonymous Mon 20 Dec 04:11:22 2021 No.13985716 View Reply Original Report

Quoted By: >>13985748 >>13985753 >>13986339 >>13987330 >>13987627 >>13989010 >>13989024 >>13989041

Are you intelligent enough to prove that this equation is true?

Anonymous

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Anonymous Mon 20 Dec 2021 04:14:36 No.13985727 Report

Quoted By: >>13988855

I did that using some Plancherel thingy or something like a million lifetimes ago.

Anonymous

Anonymous Mon 20 Dec 2021 04:19:37 No.13985748 Report

Quoted By:

>>13985716
pi is a ratio between the circumference and the diameter

Anonymous

Anonymous Mon 20 Dec 2021 04:20:24 No.13985753 Report

Quoted By: >>13985818 >>13986350 >>13987342 >>13987834 >>13988073 >>13989589

>>13985716
>...
What do "mathematicians" mean by this. What is the logical and rigorous definition for magic three dot?

Anonymous

Anonymous Mon 20 Dec 2021 04:37:52 No.13985818 Report

Quoted By: >>13988862

>>13985753
That the pattern continues infinitely.

Anonymous

Anonymous Mon 20 Dec 2021 07:00:24 No.13986280 Report

Quoted By:

That's a famous equation, I remember its proof by memory

Anonymous

Anonymous Mon 20 Dec 2021 07:11:47 No.13986315 Report

Quoted By:

This proof is so elementary, that I literally proved it in elementary school.

Anonymous

Anonymous Mon 20 Dec 2021 07:18:39 No.13986339 Report

Quoted By:

>>13985716
>try it for 1000 terms
>it doesnt converge
that equation isnt true op
>t. engineer

Anonymous

Anonymous Mon 20 Dec 2021 07:23:10 No.13986350 Report

Quoted By: >>13988862

>>13985753
$\displaystyle 0. \bar{0}1 = \lim_{n \to \infty} 0. \underbrace{0 \dots 0}_{n ~ \text{times}}1 = \lim_{n \to \infty} \left [ \left ( \sum_{k=1}^n \dfrac{0}{10^k} \right ) + \dfrac{1}{10^{n+1}} \right ] =0 $

Anonymous

Anonymous Mon 20 Dec 2021 14:32:57 No.13987330 Report

Quoted By:

>>13985716
If I can't simplify the quantity to a short hand algorithm no. But I can gleam that the answer lies in a factorial of all possible squares.

Anonymous

Anonymous Mon 20 Dec 2021 14:36:53 No.13987342 Report

Quoted By: >>13988862

>>13985753
it means that you have to look in the next picture in order to see the rest of the sequence, but OP didn't upload it yet

Anonymous

Anonymous Mon 20 Dec 2021 15:55:05 No.13987627 Report

Quoted By: >>13989780

>>13985716

$\pi = \sqrt{ 6 \sum_{n=1}^{\infty} \frac{ 1 } { n^2} } \\ \implies \frac{ \pi^2 } { 6 } = \zeta(2) = \frac{1}{2} \int ^{\infty} _{0} \frac { x } { e^{x} - 1 } dx$
So the problem of show that summation is equal to pi reduces to computing $\zeta(2)$ , which is already solved. However the integral is trivial and is indeed equal to pi^2/6.

Anonymous

Anonymous Mon 20 Dec 2021 16:57:49 No.13987834 Report

Quoted By: >>13988862

>>13985753
an abbreviation for a pattern which is clear from the context. in this case $\dots = \sum_{n=13}^{\infty} \frac{1}{n^2}$ .

Anonymous

Anonymous Mon 20 Dec 2021 18:01:36 No.13988073 Report

Quoted By: >>13988862

>>13985753
Union over a countably infinite indexing set isomorphic to N.

Anonymous

Anonymous Mon 20 Dec 2021 21:04:05 No.13988855 Report

Quoted By: >>13989972

>>13985727

Good knowledge.

It is true. You have to develop the mapping $[0, 2\pi] \rightarrow \mathbf{R} , f(x) \mapsto 1 - \frac{x}{ \pi }$ in Fourier series and use Plancherel Theorem. You will find the value

Anonymous

Anonymous Mon 20 Dec 2021 21:05:21 No.13988862 Report

Quoted By: >>13990013

>>13985818
>>13986350
>>13987342
>>13987834
>>13988073
Not rigorous.

Anonymous

Anonymous Mon 20 Dec 2021 21:33:07 No.13989010 Report

Quoted By:

>>13985716
Yeah I did this in my first year probability course.

Anonymous

Anonymous Mon 20 Dec 2021 21:35:59 No.13989024 Report

Quoted By:

>>13985716
Just draw a circle somewhere.
1/x^2 is distance shit of a field or smth.
Add them all up, get a new circle whatever who gives a shit.

Anonymous

Anonymous Mon 20 Dec 2021 21:40:05 No.13989041 Report

Quoted By:

>>13985716
No but I’m strong enough and mean enough to beat you to death if you disagree with me when I tell you it’s true.

Haha I’m just kiddin around the real answer is no

Anonymous

Anonymous Tue 21 Dec 2021 00:25:32 No.13989589 Report

Quoted By:

>>13985753
>What is the logical and rigorous definition for magic three dot
Let the reader not be a faggot…

Anonymous

Anonymous Tue 21 Dec 2021 01:28:30 No.13989780 Report

Quoted By: >>13989806

>>13987627
I know that but how do you prove it that it's pi^2/6. I mean like with elementary level math not with any fancy integrals.

Anonymous

Anonymous Tue 21 Dec 2021 01:38:06 No.13989806 Report

Quoted By:

>>13989780
>elementary level math
Do some hand wavey Euler shit. It's called the Basel problem if you want to Google it, see how Euler did it.

Anonymous

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Anonymous Tue 21 Dec 2021 02:38:12 No.13989972 Report

Quoted By: >>13989993

>>13988855
Thanks! It was most likely that function. I just remember using Parseval or Plancherel to get the $\frac{\pi^2}{6} = \sum\limits_{n=1}^\infty \frac{1}{n^2}$ when I did my then boyfriend's homework while he was busy with other stuff.

Anonymous

Anonymous Tue 21 Dec 2021 02:50:18 No.13989993 Report

Quoted By:

>>13989972
Did he suck your feminine penis afterward?

Anonymous

Anonymous Tue 21 Dec 2021 03:01:02 No.13990013 Report

Quoted By:

>>13988862
Not smart

Anonymous

Anonymous Tue 21 Dec 2021 09:21:44 No.13990882 Report

Quoted By:

I got it pretty much spoonfed in my Analysis III. There was some transition to sine i dont remeber. I can always consult a proper book

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