Does this solution have any actual physical meaning...

>Ramanujan summationis a technique invented by the mathematicianSrinivasa Ramanujanfor assigning a value todivergentinfinite series. Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties which make it mathematically useful in the study of divergentinfinite series, for which conventional summation is undefined.

So basically he's overrated shitskin pajeet?

For starter, infinuty does not exist.
Secondly, Mr curry just rearranged an "infinite" series that after a few hundred operations approx. -1/12

Geez, mathematics is so underwhelming.

Wikipedia and youtube. Thanks, guys.

lrn2read

Ramanujan is a meme

Pajeet's proof:
[math]c = 1+2+3+4+5+6+\cdots\\
4c = 0 + 4 + 0 + 8 + 0 + 12 + \cdots\\
c - 4c = -3c = 1-2+3-4+5-6+\cdots = \frac{1}{(1+1)^2} = \frac{1}{4}\\
c = -\frac{1}{12}[/math]

okay so want my original answer?

Go on

its analysis which i call magical logic it make sense for those with high iq

What's the iq cutoff to understand something like this?

180 is the minimum even then you m8 have some problems understanding it without guidance

the series diverges, the ramanujan version pretty much has no implication in any analysis subject

Wrong

but 1-2+3-4+5-6... is obviously not convergent so you're missing a huge chunk of proof there, bud

look up his proof. that is literally it`

I heard it has something to do with the Casimir effect, but I'm no expert

wasn't this on numberphile? the proof started off with proving 1-1+1-1+....=1/2, then solved some other ones to get sum of all naturals is -1/12.

>Implying wikipedia and youtube aren't diverse media platforms that contain a lot of high quality information across a broad range of topics

Ramanujans retardation is only possible because mathleticians believe infinity has a rigorous, consistent definition and further believe sensible finiteness can be extracted from values afflicted with an infinite property.

Complex analysis you fucking idiots.

That being said, because it abuses something that doesn't physically make sense that being infinite summation, the summation of -1/12 is also fruitless towards any real endeavors. It only exists for mathlets and brainlets so they can pretend to know something.

I have my own working interpretation of what's going on physically with this divergent sum and the Casimir effect. It's obviously speculative but I haven't heard of a better one yet. First, a little prereq:

In QFT, you can treat particle fields as a bunch of harmonic oscillators in space, where there exists a harmonic oscillator for each available 'mode' of the field (in momentum representation).

However, a quantum harmonic oscillator has non-zero ground state energy, meaning that there is infinite energy density in a vacuum. This is ok though since the philosophy here is that you can only measure energy differences.

In free space we have a continuous spectrum of modes for these oscillators to live on, however, if we take two metal plates and stick them together (assuming the plates act like an energy barrier like a photon field would with a perfect conductor) the spectrum becomes discrete. Wavelengths can only be half-integer multiples of the length between the plates. The energy density is still infinite, but you're missing all the modes in-between the discrete spectrum. If you take the difference, you find net negative pressure in between plates and hence a force.

The calculation for this can be found on page 27 here: damtp.cam.ac.uk/user/tong/qft/two.pdf

Now my working interpretation of divergent sums (pulled directly from my ass) is that the value obtained is what you're left over when you take out the infinity.

For example, the partial sum:

[math]S_n(a)=1+a+a^2+...+a^n=\frac{1-a^(n+1)}{1-a}[/math]

For a>1, the denominator diverges as we get larger. However, if we subtract off the part that goes to infinity, we get the usual 'values' of divergent sums.

[math]S_{\infty}(2)=1+2+4+...=-1[/math]

This makes sense to me in Casimir effect since you're subtracting off the infinite external vacuum energy to the internal vacuum energy to get net pressure.

>Fixing equations

[math]S_n(a)=1+a+a^2+...+a^n=\frac{1-a^{n+1}}{1-a}[\math]

[math]S_{\infty}(2)=1+2+3+...=-1[\math]

>Everytime

[math]S_n(a)=1+a+a^2+...+a^n=\frac{1-a^{n+1}}{1-a}[/math]
[math]S_{\infty}(2)=1+2+3+...=-1[/math]

Fuck it

Can I get a brainlet tldr of the casmir effect so I don't have to read this entire wikipedia article to understand your post?

>There is infinite energy out side the plates.

>There is infinite energy inside the plates, yet smaller than the energy outside by a finite amount.

>The energy difference is finite, which creates inward pressure

wolfram says so, so I guess we're fucked

[math] \displaystyle
\lim_{s\rightarrow 0} \left ( \sum_{x=1}^{ \infty}x^{1-s} \right )
[/math]

what was the input text for wolfram?

yeah, but the fact that isn't convergent is why the proof is wrong

What an absolute fucking wreck of a post.

math.stackexchange.com/questions/1327812/limit-approach-to-finding-1234-ldots

Also divergent sums and regularization are widely used in QFT as pointed out by
See
en.wikipedia.org/wiki/Regularization_(physics)

sum x for x=1 to infinity

I'm a brainlet, but I think these are equivalent?