Question

Prove a strong inequality $\sum_{k=1}^n\frac{k}{a_1+a_2+\cdots+a_k}\le\left(2-\frac{7\ln 2}{8\ln n}\right)\sum_{k=1}^n\frac 1{a_k}$

score 1.1k · Answer 1 · 2026-03-27 19:33:38

1.1k

Views

Prove a strong inequality $\sum_{k=1}^n\frac{k}{a_1+a_2+\cdots+a_k}\le\left(2-\frac{7\ln 2}{8\ln n}\right)\sum_{k=1}^n\frac 1{a_k}$

Published on 27 Mar 2026 - 19:33

score 370 · Answer 2 · 2026-03-26 11:05:09

370

Views

$w = \log z$ is analytic on $D = \{z : \alpha < \arg z < \alpha +2\pi k\}$

Published on 26 Mar 2026 - 11:05

score 93 · Answer 3 · 2026-04-01 12:31:01

93

Views

Calculate $\sum_{n\ge2}\log\left(1-\frac1{n^2}\right)$

Published on 01 Apr 2026 - 12:31

score 78 · Answer 4 · 2026-03-30 00:05:30

78

Views

Taylor expansion of $\log \frac{1+\exp(u+h)}{1+ \exp(u)}$

Published on 30 Mar 2026 - 0:05

score 246 · Answer 5 · 2018-10-14 06:30:32

246

Views

Convergence of the series $\sum\limits_{n=1}^{\infty}\frac1n\log\left(1+\frac1n\right)$.

Published on 14 Oct 2018 - 6:30

score 462 · Answer 6 · 2018-10-14 08:33:01

462

Views

How to simplify $\ln |\ln y | = \ln|x|+C$?

Published on 14 Oct 2018 - 8:33

score 82 · Answer 7 · 2018-10-14 17:41:05

82

Views

Difference between $\log (x^2)$ and $2\log x$

Published on 14 Oct 2018 - 17:41

score 357 · Answer 8 · 2026-03-28 07:44:08

357

Views

Exponents and Log

Published on 28 Mar 2026 - 7:44

score 70 · Answer 9 · 2018-10-16 14:33:37

70

Views

Natural Logarithmic Equation, why is my answer invalid?

Published on 16 Oct 2018 - 14:33

score 154 · Answer 10 · 2026-03-28 10:56:03

154

Views

Rewriting this exponential in terms of n

Published on 28 Mar 2026 - 10:56

score 492 · Answer 11 · 2018-10-16 20:08:08

492

Views

Using log tables for exponential solutions

Published on 16 Oct 2018 - 20:08

score 488 · Answer 12 · 2018-10-18 03:04:03

488

Views

For which values of $x$ does $y = \log_e (x - 4)$ become negative?

Published on 18 Oct 2018 - 3:04

score 30 · Answer 13 · 2018-10-18 11:30:03

30

Views

How can I find the logarithmic function of my graph?

Published on 18 Oct 2018 - 11:30

score 8.7k · Answer 14 · 2018-10-18 21:42:01

8.7k

Views

Using log table to solve a division problem

Published on 18 Oct 2018 - 21:42

score 204 · Answer 15 · 2018-10-19 17:06:31

204

Views

Is this a proof of "$\log(a^x) = x\log(a)$"?

Published on 19 Oct 2018 - 17:06

List Question

Prove a strong inequality $\sum_{k=1}^n\frac{k}{a_1+a_2+\cdots+a_k}\le\left(2-\frac{7\ln 2}{8\ln n}\right)\sum_{k=1}^n\frac 1{a_k}$

$w = \log z$ is analytic on $D = \{z : \alpha < \arg z < \alpha +2\pi k\}$

Calculate $\sum_{n\ge2}\log\left(1-\frac1{n^2}\right)$

Taylor expansion of $\log \frac{1+\exp(u+h)}{1+ \exp(u)}$

Convergence of the series $\sum\limits_{n=1}^{\infty}\frac1n\log\left(1+\frac1n\right)$.

How to simplify $\ln |\ln y | = \ln|x|+C$?

Difference between $\log (x^2)$ and $2\log x$

Exponents and Log

Natural Logarithmic Equation, why is my answer invalid?

Rewriting this exponential in terms of n

Using log tables for exponential solutions

For which values of $x$ does $y = \log_e (x - 4)$ become negative?

How can I find the logarithmic function of my graph?

Using log table to solve a division problem

Is this a proof of "$\log(a^x) = x\log(a)$"?

Trending Questions

Popular # Hahtags

Popular Questions