Question

The name of the sum $\sum_{i=0}^n \frac{1}{m-i}$

score 96 · Answer 1 · 2016-01-17 00:44:57

96

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The name of the sum $\sum_{i=0}^n \frac{1}{m-i}$

Published on 17 Jan 2016 - 0:44

score 83 · Answer 2 · 2016-01-20 17:52:09

83

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Is $\lim_{n\to\infty}a\log n-\sum_{k=n^a+1}^{n^{a+1}}\frac{1}{k}=0$ for each integer $a\geq 1$?

Published on 20 Jan 2016 - 17:52

score 430 · Answer 3 · 2016-01-25 10:52:26

430

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Find the sum of the series (rearranged harmonic series)

Published on 25 Jan 2016 - 10:52

score 138 · Answer 4 · 2016-02-01 09:43:44

138

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Prove inequality $1 < \frac{1}{n} + \frac{1}{n+1} + \ldots + \frac{1}{3n-1} < 2$

Published on 01 Feb 2016 - 9:43

score 250 · Answer 5 · 2016-02-04 19:16:53

250

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Consecutive prime numerators of harmonic numbers?

Published on 04 Feb 2016 - 19:16

score 1.3k · Answer 6 · 2016-02-04 21:44:27

1.3k

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Tough definite integral: $\int_0^\frac{\pi}{2}x\ln^2(\sin x)~dx$

Published on 04 Feb 2016 - 21:44

score 280 · Answer 7 · 2016-02-05 08:18:53

280

Views

Denominators of harmonic numbers: asymptotic behaviour.

Published on 05 Feb 2016 - 8:18

score 186 · Answer 8 · 2016-02-06 09:28:02

186

Views

Prove that $\frac 12\leq \frac{1}{n+1}+\frac {1}{n+2}+\frac{1}{n+3}...+\frac{1}{n+n}$

Published on 06 Feb 2016 - 9:28

score 3.2k · Answer 9 · 2016-02-11 20:07:54

3.2k

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Showing that Harmonic numbers are $\Theta(\log n)$, intuitively

Published on 11 Feb 2016 - 20:07

score 169 · Answer 10 · 2016-02-14 22:17:02

169

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How to prove the identity $\sum_{n=1}^{\infty} \dfrac{{H_{n}}^2}{n^2} = \dfrac{17}{360} {\pi}^4$?

Published on 14 Feb 2016 - 22:17

score 191 · Answer 11 · 2016-02-17 08:01:58

191

Views

How would look a harmonic and p-harmonic series vector in a multidimensional space?

Published on 17 Feb 2016 - 8:01

score 99 · Answer 12 · 2016-02-18 20:24:42

99

Views

What was the name of the theorem which states $\frac{1}{1}+\frac{1}{2}+...\frac{1}{p-1}\equiv 0 \pmod{p^2}$?

Published on 18 Feb 2016 - 20:24

score 6.2k · Answer 13 · 2016-02-19 04:02:45

6.2k

Views

Show $\sum_\limits{k=1}^{\infty}1/k$ does not converge.

Published on 19 Feb 2016 - 4:02

score 238 · Answer 14 · 2016-02-20 07:08:54

238

Views

An integral to prove that $\log(2n+1) \ge H_n$

Published on 20 Feb 2016 - 7:08

score 390 · Answer 15 · 2016-03-11 20:58:29

390

Views

How to prove that $a \cdot b$ is not divisible by 5 for $\frac{1}{1} + \frac{1}{2} + ... + \frac{1}{99} + \frac{1}{100} = \frac{a}{b}$?

Published on 11 Mar 2016 - 20:58

List Question

The name of the sum $\sum_{i=0}^n \frac{1}{m-i}$

Is $\lim_{n\to\infty}a\log n-\sum_{k=n^a+1}^{n^{a+1}}\frac{1}{k}=0$ for each integer $a\geq 1$?

Find the sum of the series (rearranged harmonic series)

Prove inequality $1 < \frac{1}{n} + \frac{1}{n+1} + \ldots + \frac{1}{3n-1} < 2$

Consecutive prime numerators of harmonic numbers?

Tough definite integral: $\int_0^\frac{\pi}{2}x\ln^2(\sin x)~dx$

Denominators of harmonic numbers: asymptotic behaviour.

Prove that $\frac 12\leq \frac{1}{n+1}+\frac {1}{n+2}+\frac{1}{n+3}...+\frac{1}{n+n}$

Showing that Harmonic numbers are $\Theta(\log n)$, intuitively

How to prove the identity $\sum_{n=1}^{\infty} \dfrac{{H_{n}}^2}{n^2} = \dfrac{17}{360} {\pi}^4$?

How would look a harmonic and p-harmonic series vector in a multidimensional space?

What was the name of the theorem which states $\frac{1}{1}+\frac{1}{2}+...\frac{1}{p-1}\equiv 0 \pmod{p^2}$?

Show $\sum_\limits{k=1}^{\infty}1/k$ does not converge.

An integral to prove that $\log(2n+1) \ge H_n$

How to prove that $a \cdot b$ is not divisible by 5 for $\frac{1}{1} + \frac{1}{2} + ... + \frac{1}{99} + \frac{1}{100} = \frac{a}{b}$?

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