List questions from harmonic-numbers

Published on 22 Nov 2015 - 6:51

111

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Generalized Harmonic numbers

Published on 30 Nov 2015 - 5:33

287

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Evaluation of $\sum_{n=0}^{\infty}\frac{1}{(n^4+n^2+1)n!}$

Published on 13 Dec 2015 - 23:07

72

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Expressing Express $\lim_{n\to∞} \left(\frac1{n+1} + \frac1{n+2} + ... +\frac1{n+n}\right)$ using Riemann definite integration

Published on 15 Dec 2015 - 18:53

739

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Show that the following sequence $\{x_n\}$ is increasing and bounded above, and hence convergent.

Published on 16 Dec 2015 - 15:34

240

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Inequality for Difference Between Two Harmonic Numbers

Published on 16 Dec 2015 - 18:50

3.1k

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Assymptotics of the generalized harmonic number $H_{n,r}$ for $r < 1$

Published on 20 Dec 2015 - 16:47

198

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Evaluation of $\lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{r}{n^2+n+r}$

Published on 22 Dec 2015 - 7:52

357

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Contest math problem: $\sum_{n=1}^\infty \frac{\{H_n\}}{n^2}$

Published on 28 Dec 2015 - 2:10

126

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A binary BBP-type formula for log(23)

Published on 09 Jan 2016 - 6:53

822

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Why is $e$ close to $H_8$, closer to $H_8\left(1+\frac{1}{80^2}\right)$ and even closer to $\gamma+\log\left(\frac{17}{2}\right) +\frac{1}{10^3}$?

Published on 09 Jan 2016 - 16:26

208

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Finding a solution to $\sum _{n=1}^{n=k} \frac{1}{n^x}+\sum _{n=1}^{n=k} \frac{1}{n^y}=0$

Published on 13 Jan 2016 - 14:32

178

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Finding a solution to $\sum\limits_{n=1}^{n=k} \frac{1}{n^s}=0$

Published on 15 Jan 2016 - 14:09

74

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Three almost-integers of the form $ce^{H_a+H_b}\approx 2^k\pm1$

Published on 16 Jan 2016 - 23:36

127

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Induction proof without summation

Published on 16 Jan 2016 - 23:52

List Question

$n$'th Harmonic Number Proof

Generalized Harmonic numbers

Evaluation of $\sum_{n=0}^{\infty}\frac{1}{(n^4+n^2+1)n!}$

Expressing Express $\lim_{n\to∞} \left(\frac1{n+1} + \frac1{n+2} + ... +\frac1{n+n}\right)$ using Riemann definite integration

Show that the following sequence $\{x_n\}$ is increasing and bounded above, and hence convergent.

Inequality for Difference Between Two Harmonic Numbers

Assymptotics of the generalized harmonic number $H_{n,r}$ for $r < 1$

Evaluation of $\lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{r}{n^2+n+r}$

Contest math problem: $\sum_{n=1}^\infty \frac{\{H_n\}}{n^2}$

A binary BBP-type formula for log(23)

Why is $e$ close to $H_8$, closer to $H_8\left(1+\frac{1}{80^2}\right)$ and even closer to $\gamma+\log\left(\frac{17}{2}\right) +\frac{1}{10^3}$?

Finding a solution to $\sum _{n=1}^{n=k} \frac{1}{n^x}+\sum _{n=1}^{n=k} \frac{1}{n^y}=0$

Finding a solution to $\sum\limits_{n=1}^{n=k} \frac{1}{n^s}=0$

Three almost-integers of the form $ce^{H_a+H_b}\approx 2^k\pm1$

Induction proof without summation

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