1+2+3+4+...= -1/12 (Seriously) by Roger Pink

W3ll th3r3'5 y0ur pr0bl3m right at th3 b3g1nn1ng. Y0u'r3 try1ng t0 d0 math w1th l3tt3r5 and th1ng5 that ar3n't numb3r5.

3v3r try and 5p3ll w0rd5 w1th numb3r5 and th3n w0nd3r why th3 53nt3nc35 d0n't r3ad r1ght?

I find it interesting that in the proof they use S1= +1 - 1 + 1 - 1 + ..... and assume it equals 1/2 which makes logical and intuitive sense. But can't it just as well equal something non-intuitive that no one's discovered or "proved" which would make the proof that 1+2+3+4+... = -1/12 invalid?

While I don't have the intellectual smarts to disprove the claim, there just seems to be something wrong. If I kept giving someone a marble every second, I find it hard to swallow that at some point they would end up with not only a fraction of a marble, but a negative fraction of a marble. Then at that point, what if I gave them one more.....wouldn't they then have +11/12 of a marble?

I'm not sure what these high-fallutin mathmagicians are smoking....but it's probably still illegal in Colorado.

"but it's probably still illegal in Colorado."

Maybe so, but my kids that live in New Port Richey say it doesn't stop anyone there. Course most of them are blue hairs that moved there from places where they smoked that stuff in the 60's and 70's anyway, so what's new with that?

Come to think of it, since I know some of those blue hairs, having worked with them, I'm pretty sure the stuff they smoked back then is precisely why they think like Roger does.

Crazy stuff comes out of crazy smoke, huh?

And 42 is half of the 12

1+2= 3 while 4+2 = 6 3/6 = 1/2!

lets face it it is still all linked to 42 and whoever pushes 12 is a conspiracy theorist!

Ahh yes, 42, the answer to life, the universe and everything.

That brings to mind something I saw on a black board back in college.

2+2=5 for very large values of 2

Should that be 2+2=6 for very large values of 2?

no, not necessarily. If the large value of 2 is approx 2.5 then 2.5 and 2.5 = 5.

2.5 is very large?

It is relative to 2

There are some special types of summation such as Ramanujan and Cesaro that are counterintuitive. I've never worked with them yet, so these links should be interesting. There is concurrently an Amazon Discussion on this same series.

So this means we don't have to worry about the national debt!

We had a part time maths teacher at evening classes in the late 1950's. He was a car mechanic in the day time (he said - but we didn't believe him) and maths was a hobby to earn a bit of pocket money. He had us enthralled with his mastery of maths and his wizardry with equations!

The one thing underlying the 'tricks' he used was creating hidden zeroes in the equations - that he then used to multiply or divide - that to the unwitting (us!) produced some weird results. Multiplication being much the same as successive addition, or division being successive subtraction - as used in the videos.

And me - not a mathematician - thinks this could have happened here.

Sleight of hand!

I had always thought that if a series did not converge to a value that you couldn't treat it as if it did and use it in mathematical calculations, and this result I would have considered proof. But I can't argue with the pros.