Let's post some really strange mathematical identities.

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>>8502387
1+2+3+4+5+....=-1/12
1+1+1+1+1+...=-1/2
1-1+1-1+1-...=1/2

>>8502394
>1+2+3+4+5+....=-1/12
>1+1+1+1+1+...=-1/2

isn't 1+2+3+... just 1+(1+1)+(1+1+1)+...?

>>8502396
things are tricky when you assign a value to divergent series. normal associativity and commutativity don't apply frequently.

you would probably cover this in a 3rd or 4th course in analysis, after Real and Complex at the intro level.

>>8502394
[math]
1+1+1+1+1+... = x \\
1+(1+1+1+1+...) = 1+x \\
x = 1+x \\
x \rightarrow \infty
[/math]

>>8502394
You forgot the [math] \mathfrak{R} [/math]

>>8502394
Messing with infinities was a mistake

>>8502401
No, associativity doesn't apply to infinite sums.

>>8502401
>implying 1+1+1+1+... = 1+1+1+1+1...

>>8502387
[math] \sum_{k=1}^n k^3 = \left( \sum_{k=1}^n k \right)^2[/math]
yup, that's true :)

>>8502387
What the fuck does the double exclamation mark mean?

>>8502567
odd numbers factorial desu
can be generalised with the gamma function I think. OPs equality is a result due to gauss or Euler iirc

Pretty much anything by Ramanujan.
[math]\frac{1}{1+\frac{e^{-2\pi}}{1+\frac{e^{-4\pi}}{1+\frac{e^{-6\pi}}{1+\cdots}}%
}}=\left( \sqrt{\frac{5+\sqrt{5}}{2}}-\frac{\sqrt{5}+1}{2}\right)
\sqrt[5]{e^{2\pi}}[/math]

File: Nicomachus_theorem_3D.png (107KB, 1024x1024px)

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>>8502550
I remember seeing this one, It's called Nicomachus's theorem, and here is a good visual representation of it

File: Capture.png (87KB, 802x530px) Image search: [Google]

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>>8502600
came here to post this, so i'll post the generalizations instead

https://arxiv.org/abs/1401.7718

>>8502600
How can a human discover this on his own with no proper education? It just defies belief.