Question

Using the Euler-Maclaurin formula to approximate Euler's constant, $\gamma := \lim_{n\to\infty}\left(-\ln n+\sum_{k=0}^n\frac1n\right)$

score 950 · Answer 1 · 2026-03-22 08:30:02

950

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Using the Euler-Maclaurin formula to approximate Euler's constant, $\gamma := \lim_{n\to\infty}\left(-\ln n+\sum_{k=0}^n\frac1n\right)$

Published on 22 Mar 2026 - 8:30

score 107 · Answer 2 · 2026-03-22 20:27:53

107

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Asymptotic behaviour of Schatten $p$-norm

Published on 22 Mar 2026 - 20:27

score 125 · Answer 3 · 2018-06-25 15:31:26

125

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For any $n \in \mathbb{N}$, show that: $\frac{1}{n+1} + \frac{1}{n+2} + \ldots + \frac{1}{2n} < \frac{5}{6}$.

Published on 25 Jun 2018 - 15:31

score 179 · Answer 4 · 2018-06-29 18:22:08

179

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How to prove this question by Ramanujan?

Published on 29 Jun 2018 - 18:22

score 281 · Answer 5 · 2018-07-02 12:10:40

281

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how to get $\sum_{k=1}^\infty \arctan\biggr(\frac{10k}{(3k^2+2)(9k^2-1)}\biggr)=\log3-\frac{\pi}{4}$

Published on 02 Jul 2018 - 12:10

score 162 · Answer 6 · 2026-03-22 05:53:01

162

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Infinite/Recursive Cesàro Summation of $\zeta(1)$

Published on 22 Mar 2026 - 5:53

score 201 · Answer 7 · 2018-07-07 13:39:20

201

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Lerch transcendent and harmonic number simplification

Published on 07 Jul 2018 - 13:39

score 107 · Answer 8 · 2018-07-30 22:07:13

107

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Reciprocity of different prime numbers can approximate $1$?

Published on 30 Jul 2018 - 22:07

score 198 · Answer 9 · 2018-08-14 21:45:32

198

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Exact formula or approximation for this sum (general harmonic series $H_{n,3}$)

Published on 14 Aug 2018 - 21:45

score 272 · Answer 10 · 2018-08-15 03:36:04

272

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Card shuffling and harmonic numbers

Published on 15 Aug 2018 - 3:36

score 437 · Answer 11 · 2018-08-26 23:01:23

437

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An Euler type sum: $\sum_{n=1}^{\infty}\frac{H_n^{(2)}}{n\cdot 4^n}{2n \choose n}$, where $H_n^{(2)}=\sum\limits_{k=1}^{n}\frac{1}{k^2}$

Published on 26 Aug 2018 - 23:01

score 274 · Answer 12 · 2018-08-29 10:15:39

274

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Constant term in Stirling type formula for $\sum^N_{n=1} H_n \cdot \ln(n)$

Published on 29 Aug 2018 - 10:15

score 117 · Answer 13 · 2026-03-17 01:05:15

117

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What is the solution of normalized harmonic series based on $4/3$ between one and two?

Published on 17 Mar 2026 - 1:05

score 179 · Answer 14 · 2026-03-17 14:31:51

179

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Is there an arithmetic mean limit on the symmetrical items of the harmonic series?

Published on 17 Mar 2026 - 14:31

score 236 · Answer 15 · 2018-09-08 14:10:42

236

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Finite sums of products of harmonic numbers like $\sum_{k=1}^n H_{k} H_{2k}$

Published on 08 Sep 2018 - 14:10

List Question

Using the Euler-Maclaurin formula to approximate Euler's constant, $\gamma := \lim_{n\to\infty}\left(-\ln n+\sum_{k=0}^n\frac1n\right)$

Asymptotic behaviour of Schatten $p$-norm

For any $n \in \mathbb{N}$, show that: $\frac{1}{n+1} + \frac{1}{n+2} + \ldots + \frac{1}{2n} < \frac{5}{6}$.

How to prove this question by Ramanujan?

how to get $\sum_{k=1}^\infty \arctan\biggr(\frac{10k}{(3k^2+2)(9k^2-1)}\biggr)=\log3-\frac{\pi}{4}$

Infinite/Recursive Cesàro Summation of $\zeta(1)$

Lerch transcendent and harmonic number simplification

Reciprocity of different prime numbers can approximate $1$?

Exact formula or approximation for this sum (general harmonic series $H_{n,3}$)

Card shuffling and harmonic numbers

An Euler type sum: $\sum_{n=1}^{\infty}\frac{H_n^{(2)}}{n\cdot 4^n}{2n \choose n}$, where $H_n^{(2)}=\sum\limits_{k=1}^{n}\frac{1}{k^2}$

Constant term in Stirling type formula for $\sum^N_{n=1} H_n \cdot \ln(n)$

What is the solution of normalized harmonic series based on $4/3$ between one and two?

Is there an arithmetic mean limit on the symmetrical items of the harmonic series?

Finite sums of products of harmonic numbers like $\sum_{k=1}^n H_{k} H_{2k}$

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