108 questions linked to/from Why does $1+2+3+\cdots = -\frac{1}{12}$?
3k views

### Intuition behind $\zeta(-1)$ = $\frac{-1}{12}$ [duplicate]

When I first watched numberphile's 1+2+3+... = $\frac{-1}{12}$ I thought the sum actually equalled $\frac{-1}{12}$ without really understanding it. Recently I read some wolframalpha pages and watched ...
13k views

### Is the sum of all natural numbers $-\frac{1}{12}$? [duplicate]

My friend showed me this youtube video in which the speakers present a line of reasoning as to why $$\sum_{n=1}^\infty n = -\frac{1}{12}$$ My reasoning, however, tells me that the previous ...
7k views

### How does the sum of the series “$1 + 2 + 3 + 4 + 5 + 6\ldots$” to infinity = “$-1/12$”? [duplicate]

(I was requested to edit the question to explain why it is different that a proposed duplicate question. This seems counterproductive to do here, inside the question it self, but that is what I have ...
1k views

### Sum of all odd numbers to infinity [duplicate]

Starting from the idea that $$\sum_{n=1}^\infty n = -\frac{1}{12}$$ It's fairly natural to ask about the series of odd numbers $$\sum_{n=1}^{\infty} (2n - 1)$$ I worked this out in two different ways,...
2k views

### Is there any mathematical or physical situations that $1+2+3+\ldots\infty=-\frac{1}{12}$ shows itself? [duplicate]

I just saw the proof that $$1+2+3+\cdots=-\frac{1}{12}$$ and my brain still hurts. I completely understood the proof and my question is NOT actually about the proof itself. At the end of the proof, ...
### $1+2+3+4+5+… = -\frac{1}{12}$. Is there any intuition for this? [duplicate]
I was looking into a Numberphile video here. The guy says he was unable to find an intuition. Does there exist one? Is the premise, $1-1+1-1+...=\frac{1}{2}$, reasonable mathematically?