Question

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

score 2.2k · Answer 1 · 2026-03-25 06:12:52

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 25 Mar 2026 - 6:12

score 360 · Answer 2 · 2026-03-25 06:10:33

360

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

Published on 25 Mar 2026 - 6:10

score 408 · Answer 3 · 2026-03-25 06:13:26

408

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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 25 Mar 2026 - 6:13

score 2k · Answer 4 · 2026-03-25 06:10:11

2k

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

Published on 25 Mar 2026 - 6:10

score 76 · Answer 5 · 2026-04-01 05:54:46

76

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Interesting multiplicative Ramanujan-like q-expansions

Published on 01 Apr 2026 - 5:54

score 1k · Answer 6 · 2026-04-03 14:54:11

1k

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

Published on 03 Apr 2026 - 14:54

score 291 · Answer 7 · 2026-04-05 23:34:37

291

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Question on Ramanujan Summation

Published on 05 Apr 2026 - 23:34

score 236 · Answer 8 · 2026-03-25 06:09:58

236

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Does Ramanujan summation extend Abel summation?

Published on 25 Mar 2026 - 6:09

score 506 · Answer 9 · 2026-03-25 06:12:20

506

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

Published on 25 Mar 2026 - 6:12

score 209 · Answer 10 · 2026-04-05 18:14:20

209

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Found this identity by accident

Published on 05 Apr 2026 - 18:14

score 153 · Answer 11 · 2026-03-25 06:12:40

153

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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 25 Mar 2026 - 6:12

score 661 · Answer 12 · 2026-03-25 06:13:26

661

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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 25 Mar 2026 - 6:13

score 307 · Answer 13 · 2026-03-25 06:12:14

307

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

Published on 25 Mar 2026 - 6:12

score 308 · Answer 14 · 2026-03-25 06:10:34

308

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

Published on 25 Mar 2026 - 6:10

score 2.7k · Answer 15 · 2026-03-25 06:12:19

2.7k

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

Published on 25 Mar 2026 - 6:12

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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