Question

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

score 2.2k · Answer 1 · 2014-01-09 22:22:47

2.2k

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

Published on 09 Jan 2014 - 22:22

score 359 · Answer 2 · 2014-01-24 06:40:21

359

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What consistent rules can we use to compute sums like 1 + 2 + 3 + ...?

Published on 24 Jan 2014 - 6:40

score 407 · Answer 3 · 2014-02-24 21:15:48

407

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If the set of natural numbers is closed under addition, how can we have the result that the sum of all the natural numbers to infinity is -1/12

Published on 24 Feb 2014 - 21:15

score 2k · Answer 4 · 2014-03-05 13:06:42

2k

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A Ramanujan-like summation: is it correct? Is it extensible?

Published on 05 Mar 2014 - 13:06

score 75 · Answer 5 · 2026-03-24 05:18:18

75

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Interesting multiplicative Ramanujan-like q-expansions

Published on 24 Mar 2026 - 5:18

score 1k · Answer 6 · 2017-10-04 16:02:13

1k

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Why does $1+2+3+4+\dots=-\frac1{12}$ in a couple different ways?

Published on 04 Oct 2017 - 16:02

score 289 · Answer 7 · 2017-11-28 02:13:23

289

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Question on Ramanujan Summation

Published on 28 Nov 2017 - 2:13

score 235 · Answer 8 · 2017-11-29 01:58:19

235

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Does Ramanujan summation extend Abel summation?

Published on 29 Nov 2017 - 1:58

score 505 · Answer 9 · 2020-08-02 15:09:06

505

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Can the ramanujan summation formula be used to evaluate convergent series?

Published on 02 Aug 2020 - 15:09

score 207 · Answer 10 · 2020-08-22 05:12:49

207

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Found this identity by accident

Published on 22 Aug 2020 - 5:12

score 152 · Answer 11 · 2020-08-22 06:52:58

152

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Find $\sum_{n=1}^{\infty} \frac{n^{\sigma -1} (n+\sigma )-(n+1)^{\sigma }}{\sigma(1-\sigma)}$ for $ 0<\sigma<1$

Published on 22 Aug 2020 - 6:52

score 660 · Answer 12 · 2020-08-23 05:55:01

660

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Proving $\int_{0}^{1} \frac{\tanh^{-1}\sqrt{x(1-x)}}{\sqrt{x(1-x)}}dx=\frac{1}{3}(8C-\pi\ln(2+\sqrt{3}))$ for an identity of Srinivasa Ramanujan

Published on 23 Aug 2020 - 5:55

score 306 · Answer 13 · 2020-11-11 05:48:48

306

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What is the Ramanujan summation for the series $\sqrt[n]{2}$

Published on 11 Nov 2020 - 5:48

score 307 · Answer 14 · 2020-11-17 17:42:02

307

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Computing Ramanujan asymptotic formula from Rademacher's formula for the partition function

Published on 17 Nov 2020 - 17:42

score 2.7k · Answer 15 · 2020-11-22 12:50:39

2.7k

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Interpret "the sum of all natural numbers equal $-1/12$" without complex analysis skills

Published on 22 Nov 2020 - 12:50

List Question

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

What consistent rules can we use to compute sums like 1 + 2 + 3 + ...?

If the set of natural numbers is closed under addition, how can we have the result that the sum of all the natural numbers to infinity is -1/12

A Ramanujan-like summation: is it correct? Is it extensible?

Interesting multiplicative Ramanujan-like q-expansions

Why does $1+2+3+4+\dots=-\frac1{12}$ in a couple different ways?

Question on Ramanujan Summation

Does Ramanujan summation extend Abel summation?

Can the ramanujan summation formula be used to evaluate convergent series?

Found this identity by accident

Find $\sum_{n=1}^{\infty} \frac{n^{\sigma -1} (n+\sigma )-(n+1)^{\sigma }}{\sigma(1-\sigma)}$ for $ 0<\sigma<1$

Proving $\int_{0}^{1} \frac{\tanh^{-1}\sqrt{x(1-x)}}{\sqrt{x(1-x)}}dx=\frac{1}{3}(8C-\pi\ln(2+\sqrt{3}))$ for an identity of Srinivasa Ramanujan

What is the Ramanujan summation for the series $\sqrt[n]{2}$

Computing Ramanujan asymptotic formula from Rademacher's formula for the partition function

Interpret "the sum of all natural numbers equal $-1/12$" without complex analysis skills

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