Question

A statement about harmonic numbers from Knuth's The Art of Computer Programming

score 459 · Answer 1 · 2015-10-02 21:24:57

459

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A statement about harmonic numbers from Knuth's The Art of Computer Programming

Published on 02 Oct 2015 - 21:24

score 861 · Answer 2 · 2026-03-24 02:56:18

861

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Strategies for evaluating sums $\sum_{n=1}^\infty \frac{H_n^{(m)}z^n}{n}$

Published on 24 Mar 2026 - 2:56

score 147 · Answer 3 · 2015-10-13 18:07:43

147

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Special case of Faulhaber's formula

Published on 13 Oct 2015 - 18:07

score 74 · Answer 4 · 2026-02-28 06:29:05

74

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What are the first few values of this function?

Published on 28 Feb 2026 - 6:29

score 234 · Answer 5 · 2015-10-17 13:48:28

234

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To prove that $\sum_{k=1}^{n}{{1}\over {k}} \ge \log n$

Published on 17 Oct 2015 - 13:48

score 91 · Answer 6 · 2015-10-17 22:34:16

91

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Sum of the recripocals of the Harmonic Numbers

Published on 17 Oct 2015 - 22:34

score 608 · Answer 7 · 2015-10-21 11:26:20

608

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Prove by induction $\sum _{i=1}^n\left(-1\right)^{i+1}\:\binom{n}{i}\:\frac{1}{i}=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n}$

Published on 21 Oct 2015 - 11:26

score 107 · Answer 8 · 2015-10-26 14:37:40

107

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Prove by induction: $\left(\frac{1}{n+1}+\frac{1}{n+2}+...\frac{1}{2n}\right)^2<\frac{1}{2},n\ge 1$

Published on 26 Oct 2015 - 14:37

score 1.3k · Answer 9 · 2026-03-28 23:15:13

1.3k

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Proof of a sum with binomial coefficients $\sum_{k=1}^n (-1)^{k+1}{\binom nk}\frac{1}{k} = 1 + \frac{1}{2} + \ldots +\frac{1}{n}$

Published on 28 Mar 2026 - 23:15

score 55 · Answer 10 · 2015-10-30 19:54:00

55

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Can someone explain the cancellation in this Induction proof? (Harmonic Sequence)

Published on 30 Oct 2015 - 19:54

score 71 · Answer 11 · 2026-03-23 23:31:25

71

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Sum of divisors(n!)/n! is greater than Harmonic Number(n)

Published on 23 Mar 2026 - 23:31

score 405 · Answer 12 · 2026-03-26 17:34:00

405

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Is there a proof that the Harmonic numbers are not an elementary function?

Published on 26 Mar 2026 - 17:34

score 174 · Answer 13 · 2015-11-13 07:08:28

174

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Prove that $\frac{n+1}{2} \leq 2\cdot\sqrt{2}\cdot\sqrt[3]{2}\cdot\sqrt[4]{2}\cdots\sqrt[n]{2}$

Published on 13 Nov 2015 - 7:08

score 814 · Answer 14 · 2015-11-16 20:17:49

814

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The harmonic number of any order is not an integer

Published on 16 Nov 2015 - 20:17

score 49 · Answer 15 · 2015-11-19 10:01:09

49

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If $\lim_{n\to\infty}\frac{\ell_n}{\log n}=1$, does $n\log n\geq -C \iff (n+1)\ell_{n-1}\geq -C$ hold?

Published on 19 Nov 2015 - 10:01

List Question

A statement about harmonic numbers from Knuth's The Art of Computer Programming

Strategies for evaluating sums $\sum_{n=1}^\infty \frac{H_n^{(m)}z^n}{n}$

Special case of Faulhaber's formula

What are the first few values of this function?

To prove that $\sum_{k=1}^{n}{{1}\over {k}} \ge \log n$

Sum of the recripocals of the Harmonic Numbers

Prove by induction $\sum _{i=1}^n\left(-1\right)^{i+1}\:\binom{n}{i}\:\frac{1}{i}=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n}$

Prove by induction: $\left(\frac{1}{n+1}+\frac{1}{n+2}+...\frac{1}{2n}\right)^2<\frac{1}{2},n\ge 1$

Proof of a sum with binomial coefficients $\sum_{k=1}^n (-1)^{k+1}{\binom nk}\frac{1}{k} = 1 + \frac{1}{2} + \ldots +\frac{1}{n}$

Can someone explain the cancellation in this Induction proof? (Harmonic Sequence)

Sum of divisors(n!)/n! is greater than Harmonic Number(n)

Is there a proof that the Harmonic numbers are not an elementary function?

Prove that $\frac{n+1}{2} \leq 2\cdot\sqrt{2}\cdot\sqrt[3]{2}\cdot\sqrt[4]{2}\cdots\sqrt[n]{2}$

The harmonic number of any order is not an integer

If $\lim_{n\to\infty}\frac{\ell_n}{\log n}=1$, does $n\log n\geq -C \iff (n+1)\ell_{n-1}\geq -C$ hold?

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