Linked Questions

8
votes
7answers
2k 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 ...
4
votes
4answers
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 ...
4
votes
4answers
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 ...
1
vote
2answers
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,...
4
votes
1answer
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
vote
3answers
1k views

Does $\zeta(-1)=-1/12$ or $\zeta(-1) \to -1/12$? [duplicate]

I saw NumberPhile channel on Youtube, and they proved $1+2+3+\cdots=-1/12$. Also, I read This. So, which one is correct $$\zeta(-1)=-1/12\\ \text{or} \\\zeta(-1) \to -1/12$$ Equivalent to: $$1+2+3+...
0
votes
1answer
19k views

Sum of all the positive integers problem [duplicate]

The staff of Numberphile has shown that the sum of all the integers from $0$ to $\infty$ is $-\frac1{12}$. Recently I was looking for the sum of all the (positive) integers from $0$ to $n$ and I found ...
-3
votes
3answers
6k views

The sum of all the odd numbers to infinity [duplicate]

We have this sequence: S1: 1+2+3+4+5+6.. (to infinity) It has been demonstrated, that S1 = -1/12. Now, what happens if i multiply by a factor of 2? S2: 2+4+6+8+10+12.... (to infinity). I have 2S1,...
1
vote
2answers
1k views

Why is the sum over all positive integers equal to -1/12? [duplicate]

Recently, sources for mathematical infotainment, for example numberphile, have given some information on the interpretation of divergent series as real numbers, for example $\sum_{i=0}^\infty i = -{1 ...
3
votes
1answer
4k views

Explanation of Zeta function and why 1+2+3+4+… = -1/12 [duplicate]

Possible Duplicate: Why does $1+2+3+\dots = {-1\over 12}$? I found this article on Wikipedia which claims that $\sum\limits_{n=0}^\infty n=-1/12$. Can anyone give a simple and short summary on ...
2
votes
2answers
827 views

Why $\zeta(-2) $ is not $\sum_{n=1}^{\infty}\frac{1}{n^{-2}}$? [duplicate]

Let $\zeta(s)= \sum_{n=1}^{\infty}\frac{1}{n^{s}}$ a standard formula. I'm confused if you tell me: does this series: $\sum_{n=1}^{\infty}\frac{1} {n^{s}}$ converge? I will answer you: this series ...
1
vote
3answers
3k views

Does sum of all natural numbers contradict another rule? [duplicate]

I must say that I am not a mathematician, just a enthusiast who likes to read all the "weird" results in mathematics. I read that sum of all natural number equals to $-1/12$ and I am also aware that ...
3
votes
1answer
2k views

How is $\zeta(0)=-1/2$? [duplicate]

Possible Duplicate: Why does $1+2+3+\dots = {-1\over 12}$? Fermat's Dream by Kato et al. gives the following: $\zeta(s)=\sum\limits_{n=1}^{\infty}\frac{1}{n^s}$ (the standard Zeta function) ...
1
vote
5answers
221 views

Where is the mistake in proving 1+2+3+4+… = -1/12? [duplicate]

https://www.youtube.com/watch?v=w-I6XTVZXww#t=30 As I watched the video on YouTube of proving sum of $$1+2+3+4+\cdots= \frac{-1}{12}$$ Even we know that the series does not converge. First I still ...
0
votes
3answers
301 views

$1+2+3+4+5+… = -\frac{1}{12}$. 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?

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