List questions from harmonic-numbers

Published on 25 Jul 2016 - 13:06

84

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Find the value of: $\lim_{n \to \infty}\left(\frac{1}{n+1}+\cdots+\frac{1}{2n}\right)$

Published on 01 Aug 2016 - 22:32

489

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Alternating Euler sums

Published on 05 Aug 2016 - 6:14

73

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On $\sigma(n)=\sigma \left( \left \lfloor{e^{H_n-\gamma}}\right \rfloor \right) $, for integers $n\geq 1$

Published on 09 Aug 2016 - 8:25

107

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Can you provide us calculations for an upper bound of $\frac{15}{\pi^2}ne^{H_n}\log(H_n)-e^{H_{n^2}}\log(H_{n^2})$?

Published on 09 Aug 2016 - 17:27

94

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A harmonic sum with 'k'

Published on 09 Aug 2016 - 18:27

252

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ODE and raw moments

Published on 12 Aug 2016 - 15:03

73

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Smallest $n$ such that $H_{n,2^{-1}} \geq n$ where $H_{n,2^{-1}}$ are generalized Harmonic numbers

Published on 17 Aug 2016 - 22:19

152

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Solving limit $\lim_{n\rightarrow \infty} (\frac{1}{n+1}+ ... +\frac{1}{2n})$

Published on 18 Aug 2016 - 9:08

242

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Does make sense a generalization of Lagarias equivalence with $H_n^s=1+1/2^s+\ldots+1/n^s$ and $\sigma^s(n)=\sum_{k\mid n}k^s$, for $\Re s>1$?

Published on 26 Mar 2026 - 8:02

401

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Simplifying $\sum_{i=1}^n{\lfloor \frac{n}{i} \rfloor}$?

Published on 19 Aug 2016 - 23:54

120

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This number is not natural

Published on 21 Aug 2016 - 1:07

1.2k

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Notation For Summation of Factorials

Published on 22 Aug 2016 - 5:40

45

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How do we find the series expansion for $H_n^{(-1/2)}$

Published on 24 Aug 2016 - 18:28

1.4k

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Reference for the rate of divergence of Harmonic series

Published on 01 Sep 2016 - 7:00

List Question

Prove the inequality between integral and summation of multiplicative inverse

Find the value of: $\lim_{n \to \infty}\left(\frac{1}{n+1}+\cdots+\frac{1}{2n}\right)$

Alternating Euler sums

On $\sigma(n)=\sigma \left( \left \lfloor{e^{H_n-\gamma}}\right \rfloor \right) $, for integers $n\geq 1$

Can you provide us calculations for an upper bound of $\frac{15}{\pi^2}ne^{H_n}\log(H_n)-e^{H_{n^2}}\log(H_{n^2})$?

A harmonic sum with 'k'

ODE and raw moments

Smallest $n$ such that $H_{n,2^{-1}} \geq n$ where $H_{n,2^{-1}}$ are generalized Harmonic numbers

Solving limit $\lim_{n\rightarrow \infty} (\frac{1}{n+1}+ ... +\frac{1}{2n})$

Does make sense a generalization of Lagarias equivalence with $H_n^s=1+1/2^s+\ldots+1/n^s$ and $\sigma^s(n)=\sum_{k\mid n}k^s$, for $\Re s>1$?

Simplifying $\sum_{i=1}^n{\lfloor \frac{n}{i} \rfloor}$?

This number is not natural

Notation For Summation of Factorials

How do we find the series expansion for $H_n^{(-1/2)}$

Reference for the rate of divergence of Harmonic series

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