Question

Harmonic Series Convergence

score 2.3k · Answer 1 · 2016-12-01 08:56:27

2.3k

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Harmonic Series Convergence

Published on 01 Dec 2016 - 8:56

score 116 · Answer 2 · 2026-03-25 12:54:29

116

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$\lim_{N\rightarrow\infty}\left< \psi{\left(N_k+1\right)} - \psi{\left(N_j+1\right)} \right >$

Published on 25 Mar 2026 - 12:54

score 523 · Answer 3 · 2016-12-07 00:53:22

523

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Probability Question with Harmonic series

Published on 07 Dec 2016 - 0:53

score 121 · Answer 4 · 2016-12-08 05:01:22

121

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Sum of Harmonic Number error over all $n$

Published on 08 Dec 2016 - 5:01

score 135 · Answer 5 · 2016-12-09 02:14:29

135

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Alternate asymptotics for the Harmonic Numbers

Published on 09 Dec 2016 - 2:14

score 1.2k · Answer 6 · 2026-03-27 20:31:19

1.2k

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there exist infinite many $n\in\mathbb{N}$ such that $S_n-[S_n]<\frac{1}{n^2}$

Published on 27 Mar 2026 - 20:31

score 106 · Answer 7 · 2016-12-21 17:14:44

106

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Summation Formula for Series

Published on 21 Dec 2016 - 17:14

score 189 · Answer 8 · 2016-12-22 17:11:24

189

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Prove without induction that $\sum_{r=1}^n {n\choose r}(-1)^{r+1}\frac1r=\sum_{r=1}^n \frac1r$

Published on 22 Dec 2016 - 17:11

score 675 · Answer 9 · 2016-12-25 09:41:30

675

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Prove A New Method For Finding Primes.

Published on 25 Dec 2016 - 9:41

score 273 · Answer 10 · 2016-12-26 11:13:24

273

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Show that :$\sum_{j=0}^{n}j{n\choose j}^2H_{n-j}={1\over 4}{2n\choose n}(4nH_{n}-2nH_{2n}-1)$

Published on 26 Dec 2016 - 11:13

score 453 · Answer 11 · 2026-03-25 22:42:08

453

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Prove that for each $n \in \mathbb N$, $\gamma_n=1+\frac{1}{2}+\dots+\frac{1}{n}-\int_1^n \frac{1}{x}dx$ is convergent

Published on 25 Mar 2026 - 22:42

score 185 · Answer 12 · 2026-03-25 22:06:09

185

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Prove that:$(\phi-1)^1(2-\phi)^{1\over4}(2\phi-3)^{1\over9}(5-3\phi)^{1\over16}\cdots(F_{n+1}-\phi F_n)^{1\over n^2}=\phi^{-H_n}$

Published on 25 Mar 2026 - 22:06

score 97 · Answer 13 · 2016-12-29 20:25:04

97

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Show that : $\sum_{k=0}^{n}{(-1)^k{n\choose k}\over (k+1)^2}={1+\sqrt{1+4(n+1)^2H_nH_{n+1}}\over 2(n+1)^2}$, for $n\ge0$

Published on 29 Dec 2016 - 20:25

score 189 · Answer 14 · 2016-12-30 08:20:49

189

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How can we show that : $\sum\limits_{n=1}^{\infty}{H_{n,2}\over n^2}={7\over4}\cdot\zeta(4)$

Published on 30 Dec 2016 - 8:20

score 937 · Answer 15 · 2017-01-01 06:03:30

937

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Convergence of harmonic series multiplied by partial sums of harmonic series

Published on 01 Jan 2017 - 6:03

List Question

Harmonic Series Convergence

$\lim_{N\rightarrow\infty}\left< \psi{\left(N_k+1\right)} - \psi{\left(N_j+1\right)} \right >$

Probability Question with Harmonic series

Sum of Harmonic Number error over all $n$

Alternate asymptotics for the Harmonic Numbers

there exist infinite many $n\in\mathbb{N}$ such that $S_n-[S_n]<\frac{1}{n^2}$

Summation Formula for Series

Prove without induction that $\sum_{r=1}^n {n\choose r}(-1)^{r+1}\frac1r=\sum_{r=1}^n \frac1r$

Prove A New Method For Finding Primes.

Show that :$\sum_{j=0}^{n}j{n\choose j}^2H_{n-j}={1\over 4}{2n\choose n}(4nH_{n}-2nH_{2n}-1)$

Prove that for each $n \in \mathbb N$, $\gamma_n=1+\frac{1}{2}+\dots+\frac{1}{n}-\int_1^n \frac{1}{x}dx$ is convergent

Prove that:$(\phi-1)^1(2-\phi)^{1\over4}(2\phi-3)^{1\over9}(5-3\phi)^{1\over16}\cdots(F_{n+1}-\phi F_n)^{1\over n^2}=\phi^{-H_n}$

Show that : $\sum_{k=0}^{n}{(-1)^k{n\choose k}\over (k+1)^2}={1+\sqrt{1+4(n+1)^2H_nH_{n+1}}\over 2(n+1)^2}$, for $n\ge0$

How can we show that : $\sum\limits_{n=1}^{\infty}{H_{n,2}\over n^2}={7\over4}\cdot\zeta(4)$

Convergence of harmonic series multiplied by partial sums of harmonic series

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