List questions from harmonic-numbers

Published on 12 Mar 2016 - 16:05

533

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Doubt on limit of sum of sequences. Two procedures leads to different answers.

Published on 13 Mar 2016 - 22:15

94

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Prove that $1+\frac12+\frac13+\cdots+\frac1{2^n} \ge 1+\frac{n}{2}$

Published on 19 Mar 2016 - 0:55

178

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Prove $\frac{1}{n} + \frac{1}{n+1} + .... + \frac{1}{2n} > 0.63 $

Published on 19 Mar 2016 - 12:00

150

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$\sum_{n = 1}^\infty (-1)^n \frac{H_n}{n^s}$ in terms of $\sum_{n = 1}^\infty \frac{H_n}{n^s}$

Published on 27 Mar 2016 - 12:01

344

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Integral $\int_0^1\frac{\ln(1-x)}{x}\text{Li}_3\left({x} \right)\,dx$

Published on 27 Mar 2026 - 22:12

115

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An Identity with Binomials and Harmonic Numbers

Published on 05 Apr 2016 - 9:06

132

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How to evaluate $\lim_{n\rightarrow \infty }n\left [ \widetilde{H_{n}}-H_{2n}+H_n \right ]$?

Published on 06 Apr 2016 - 12:24

184

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Show that $H_n$ is almost always a non-terminating decimal.

Published on 08 Apr 2016 - 14:55

401

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asymptotic equivalence between harmonic numbers and logarithm

Published on 08 Apr 2016 - 14:55

751

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Test for the convergence of the sequence $S_n =\frac1n \left(1 + \frac{1}{2} + \frac{1}{3} + \cdots+ \frac{1}{n}\right)$

Published on 25 Apr 2016 - 10:50

43

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Harmonic Numbers give Odd Constant

Published on 02 May 2016 - 2:27

474

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Harmonic mean and arithmetic mean

Published on 09 May 2016 - 7:37

272

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What's about $\sum_{n=1}^{\infty} \frac{e^{H_n}\log H_n}{n^3}$, where $H_n$ is the nth harmonic number?

Published on 11 May 2016 - 7:11

183

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Prove that $\sum_{j=0}^{n}H_j{n\choose j}^2={2n\choose n}\left(2H_n-H_{2n}\right)$

Published on 24 May 2016 - 22:59

List Question

Presentation of the unit

Doubt on limit of sum of sequences. Two procedures leads to different answers.

Prove that $1+\frac12+\frac13+\cdots+\frac1{2^n} \ge 1+\frac{n}{2}$

Prove $\frac{1}{n} + \frac{1}{n+1} + .... + \frac{1}{2n} > 0.63 $

$\sum_{n = 1}^\infty (-1)^n \frac{H_n}{n^s}$ in terms of $\sum_{n = 1}^\infty \frac{H_n}{n^s}$

Integral $\int_0^1\frac{\ln(1-x)}{x}\text{Li}_3\left({x} \right)\,dx$

An Identity with Binomials and Harmonic Numbers

How to evaluate $\lim_{n\rightarrow \infty }n\left [ \widetilde{H_{n}}-H_{2n}+H_n \right ]$?

Show that $H_n$ is almost always a non-terminating decimal.

asymptotic equivalence between harmonic numbers and logarithm

Test for the convergence of the sequence $S_n =\frac1n \left(1 + \frac{1}{2} + \frac{1}{3} + \cdots+ \frac{1}{n}\right)$

Harmonic Numbers give Odd Constant

Harmonic mean and arithmetic mean

What's about $\sum_{n=1}^{\infty} \frac{e^{H_n}\log H_n}{n^3}$, where $H_n$ is the nth harmonic number?

Prove that $\sum_{j=0}^{n}H_j{n\choose j}^2={2n\choose n}\left(2H_n-H_{2n}\right)$

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