Question

What is $\sum_{i=1}^{r} (i^{-1/3})$?.

score 55 · Answer 1 · 2016-10-09 18:30:02

55

Views

What is $\sum_{i=1}^{r} (i^{-1/3})$?.

Published on 09 Oct 2016 - 18:30

score 1.2k · Answer 2 · 2016-10-10 03:56:23

1.2k

Views

Find the limit of the following expression:

Published on 10 Oct 2016 - 3:56

score 57 · Answer 3 · 2016-10-13 16:18:35

57

Views

How do I show, when $n$ is large, that the Harmonic number is approx $\log n$?

Published on 13 Oct 2016 - 16:18

score 1k · Answer 4 · 2026-03-25 17:44:45

1k

Views

Prove that $\frac{\frac{1}{11}+\frac{1}{12}+\dots+\frac{1}{200}}{\frac{1}{1011}+\frac{1}{1112}+\dots+\frac{1}{19*20}}>19$

Published on 25 Mar 2026 - 17:44

score 807 · Answer 5 · 2016-10-22 16:40:59

807

Views

Relation between binomial coefficients and harmonic numbers

Published on 22 Oct 2016 - 16:40

score 272 · Answer 6 · 2016-10-24 20:17:46

272

Views

Let's prove this inequality, with/without induction $\sum\limits_{i=1}^n\frac1i \le \sqrt n$

Published on 24 Oct 2016 - 20:17

score 1.2k · Answer 7 · 2016-10-30 07:55:51

1.2k

Views

Partial sum of the harmonic series between two consecutive fibonacci numbers

Published on 30 Oct 2016 - 7:55

score 210 · Answer 8 · 2026-03-25 11:54:04

210

Views

Is $\sum\limits_{n = 1}^\infty (-1)^n\frac{H_n}{n}=\frac{6\ln^2(2)-\pi^2}{12}$ a valid identity?

Published on 25 Mar 2026 - 11:54

score 78 · Answer 9 · 2016-11-10 06:17:51

78

Views

$s_n=\sum_{k=1}^n \frac{1}{k}$ then $s_n$ is bounded sequence?

Published on 10 Nov 2016 - 6:17

score 175 · Answer 10 · 2016-11-11 14:54:29

175

Views

Conjectured value of $\int_0^1 (-x^a\cos(\ln{x})\ln(1-x))\,dx$, where $a\geq-1$

Published on 11 Nov 2016 - 14:54

score 206 · Answer 11 · 2026-03-27 06:56:48

206

Views

Alternate proof of this identity for the generalized Harmonic number?

Published on 27 Mar 2026 - 6:56

score 121 · Answer 12 · 2016-11-23 14:58:18

121

Views

Proof why $\frac{1}{n^x}+\frac{1}{(n+1)^x}=\frac{H_{{n+1,x}}}{n^xH_{n,x}}+\frac{H_{{n-1,x}}}{(n+1)^xH_{n,x}}$

Published on 23 Nov 2016 - 14:58

score 83 · Answer 13 · 2026-03-26 03:13:30

83

Views

The convergence of $\sum_{n=1}^\infty\frac{\mu(n+1)}{n+1}H_{n+1}$, where $\mu(n)$ is the Möbius function and $H_n=1+1/2+\ldots+1/n$

Published on 26 Mar 2026 - 3:13

score 361 · Answer 14 · 2026-02-23 05:47:18

361

Views

On the asymptotic behaviour of the Cauchy product of harmonic numbers $\sum_{k=1}^n H_k H_{n-k+1}$

Published on 23 Feb 2026 - 5:47

score 668 · Answer 15 · 2016-11-29 17:00:17

668

Views

On the product over primes $\prod_{p \leq N} \frac{p-1}{p-2}$

Published on 29 Nov 2016 - 17:00

List Question

What is $\sum_{i=1}^{r} (i^{-1/3})$?.

Find the limit of the following expression:

How do I show, when $n$ is large, that the Harmonic number is approx $\log n$?

Prove that $\frac{\frac{1}{11}+\frac{1}{12}+\dots+\frac{1}{200}}{\frac{1}{1011}+\frac{1}{1112}+\dots+\frac{1}{19*20}}>19$

Relation between binomial coefficients and harmonic numbers

Let's prove this inequality, with/without induction $\sum\limits_{i=1}^n\frac1i \le \sqrt n$

Partial sum of the harmonic series between two consecutive fibonacci numbers

Is $\sum\limits_{n = 1}^\infty (-1)^n\frac{H_n}{n}=\frac{6\ln^2(2)-\pi^2}{12}$ a valid identity?

$s_n=\sum_{k=1}^n \frac{1}{k}$ then $s_n$ is bounded sequence?

Conjectured value of $\int_0^1 (-x^a\cos(\ln{x})\ln(1-x))\,dx$, where $a\geq-1$

Alternate proof of this identity for the generalized Harmonic number?

Proof why $\frac{1}{n^x}+\frac{1}{(n+1)^x}=\frac{H_{{n+1,x}}}{n^xH_{n,x}}+\frac{H_{{n-1,x}}}{(n+1)^xH_{n,x}}$

The convergence of $\sum_{n=1}^\infty\frac{\mu(n+1)}{n+1}H_{n+1}$, where $\mu(n)$ is the Möbius function and $H_n=1+1/2+\ldots+1/n$

On the asymptotic behaviour of the Cauchy product of harmonic numbers $\sum_{k=1}^n H_k H_{n-k+1}$

On the product over primes $\prod_{p \leq N} \frac{p-1}{p-2}$

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