List questions from harmonic-numbers

Published on 30 Sep 2019 - 19:11

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Show that there is a real positive solution

Published on 15 Mar 2014 - 5:26

121

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Is there an infinite hierarchy of sequences whose reciprocals diverge, starting with the natural numbers?

Published on 19 Mar 2014 - 14:06

554

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Using $S_n = \sum_{k=1}^{n}H_k$ where $H_k$ are the harmonic numbers, show $S_n = (n+1)H_n - n$

Published on 19 Mar 2014 - 21:33

324

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computing the limit of $\frac{1}{n} \sum_{k=1}^{n}{\frac{1}{k}}$

Published on 20 Mar 2014 - 16:10

4.8k

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Relationship between logarithms and harmonic series

Published on 23 Mar 2014 - 18:48

965

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How find this series $\sum_{n=1}^{\infty}\frac{1}{n^2H_{n}}$?

Published on 06 Apr 2014 - 0:39

220

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How to calculate $\lim_{n \to \infty} \frac 1{3n} +\frac 1{3n+1}+\cdots+\frac 1{4n}$?

Published on 10 Apr 2014 - 12:44

133

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A formula for $\sum^n_{i=1}(1+1/n)$?

Published on 13 Apr 2014 - 1:56

1.4k

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$-4\zeta(2)-2\zeta(3)+4\zeta(2)\zeta(3)+2\zeta(5)=S$

Published on 20 Apr 2014 - 7:08

4.8k

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Integral $\int_0^1 dx \frac{\ln x \ln^2(1-x)\ln(1+x)}{x}$

Published on 20 Apr 2014 - 16:55

117

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Convergence of $\sum_{n=1}^{\infty}(\frac{H_n}{p_n}-\frac{n}{n^n})$

Published on 27 Apr 2014 - 15:54

374

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Two inequalities for the difference $H_n - H_m$ of harmonic numbers

Published on 29 Apr 2014 - 15:18

1.2k

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Evaluation of $\int_0^1 \frac{\log^2(1+x)}{x} \ dx$

Published on 15 May 2014 - 13:09

142

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Show that $b_n > b_{n-1}$ where $\frac{a_n}{b_n}$ are the n:th harmonic number

Published on 15 May 2014 - 18:25

List Question

Compute $\sum_{n=1}^\infty\frac{H_{n}^2}{(2n+1)^3}$

Show that there is a real positive solution

Is there an infinite hierarchy of sequences whose reciprocals diverge, starting with the natural numbers?

Using $S_n = \sum_{k=1}^{n}H_k$ where $H_k$ are the harmonic numbers, show $S_n = (n+1)H_n - n$

computing the limit of $\frac{1}{n} \sum_{k=1}^{n}{\frac{1}{k}}$

Relationship between logarithms and harmonic series

How find this series $\sum_{n=1}^{\infty}\frac{1}{n^2H_{n}}$?

How to calculate $\lim_{n \to \infty} \frac 1{3n} +\frac 1{3n+1}+\cdots+\frac 1{4n}$?

A formula for $\sum^n_{i=1}(1+1/n)$?

$-4\zeta(2)-2\zeta(3)+4\zeta(2)\zeta(3)+2\zeta(5)=S$

Integral $\int_0^1 dx \frac{\ln x \ln^2(1-x)\ln(1+x)}{x}$

Convergence of $\sum_{n=1}^{\infty}(\frac{H_n}{p_n}-\frac{n}{n^n})$

Two inequalities for the difference $H_n - H_m$ of harmonic numbers

Evaluation of $\int_0^1 \frac{\log^2(1+x)}{x} \ dx$

Show that $b_n > b_{n-1}$ where $\frac{a_n}{b_n}$ are the n:th harmonic number

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