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 959 · Answer 1 · 2026-05-02 20:26:10

959

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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 02 May 2026 - 20:26

score 112 · Answer 2 · 2026-04-29 12:42:53

112

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Asymptotic behaviour of Schatten $p$-norm

Published on 29 Apr 2026 - 12:42

score 128 · Answer 3 · 2026-04-15 17:20:50

128

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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 15 Apr 2026 - 17:20

score 184 · Answer 4 · 2026-04-11 07:06:57

184

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How to prove this question by Ramanujan?

Published on 11 Apr 2026 - 7:06

score 284 · Answer 5 · 2026-04-16 13:50:38

284

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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 16 Apr 2026 - 13:50

score 167 · Answer 6 · 2026-05-05 03:24:12

167

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

Published on 05 May 2026 - 3:24

score 204 · Answer 7 · 2026-04-15 12:39:03

204

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Lerch transcendent and harmonic number simplification

Published on 15 Apr 2026 - 12:39

score 110 · Answer 8 · 2026-04-15 03:00:33

110

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Reciprocity of different prime numbers can approximate $1$?

Published on 15 Apr 2026 - 3:00

score 200 · Answer 9 · 2026-04-13 17:12:26

200

Views

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

Published on 13 Apr 2026 - 17:12

score 278 · Answer 10 · 2026-05-07 07:41:23

278

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Card shuffling and harmonic numbers

Published on 07 May 2026 - 7:41

score 440 · Answer 11 · 2026-04-11 19:16:29

440

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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 11 Apr 2026 - 19:16

score 277 · Answer 12 · 2026-04-09 16:49:21

277

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

Published on 09 Apr 2026 - 16:49

score 122 · Answer 13 · 2026-05-03 20:43:33

122

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

Published on 03 May 2026 - 20:43

score 184 · Answer 14 · 2026-04-23 14:45:16

184

Views

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

Published on 23 Apr 2026 - 14:45

score 239 · Answer 15 · 2026-04-16 07:45:11

239

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

Published on 16 Apr 2026 - 7:45

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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