Question

Show that $\frac{1}{k}-\ln\left(\frac{k+1}{k}\right)$ is bounded by $\frac{1}{k^2}$

score 47 · Answer 1 · 2026-03-17 11:22:20

47

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Show that $\frac{1}{k}-\ln\left(\frac{k+1}{k}\right)$ is bounded by $\frac{1}{k^2}$

Published on 17 Mar 2026 - 11:22

score 99 · Answer 2 · 2026-03-22 11:37:58

99

Views

Bounding Probability with Large Variance

Published on 22 Mar 2026 - 11:37

score 1.5k · Answer 3 · 2026-03-17 15:08:56

1.5k

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How to prove the inequality $\frac{1}{n}+\frac{1}{n+1}+\cdots+\frac{1}{2n-1}\geq \log (2)$?

Published on 17 Mar 2026 - 15:08

score 77 · Answer 4 · 2026-03-22 12:13:21

77

Views

In resticted domain , Applying the Cauchy-Schwarz's inequality

Published on 22 Mar 2026 - 12:13

score 291 · Answer 5 · 2026-03-19 18:25:22

291

Views

Mean value theorem for functions from $\mathbb R^n \to \mathbb R^n$

Published on 19 Mar 2026 - 18:25

score 138 · Answer 6 · 2026-03-19 19:59:43

138

Views

for $x,y,z\ge 0$, $x+y+z=2$, prove $\frac{x}{1+y^2}+\frac{y}{1+z^2}+\frac{z}{1+x^2}\ge\frac{18}{13}$

Published on 19 Mar 2026 - 19:59

score 123 · Answer 7 · 2026-03-17 12:17:37

123

Views

If $|ax^2+bx+c|\le \frac12$ for all $|x|\le1$, then $|ax^2+bx+c|\le x^2-\frac12$ for all $|x|\ge1$

Published on 17 Mar 2026 - 12:17

score 150 · Answer 8 · 2026-03-24 11:05:55

150

Views

Interesting inequalities

Published on 24 Mar 2026 - 11:05

score 36 · Answer 9 · 2026-03-17 08:47:56

36

Views

An algebraic inequality with three components

Published on 17 Mar 2026 - 8:47

score 301 · Answer 10 · 2026-03-20 05:34:26

301

Views

Solving for the values of x when x is on both sides of a logarithmic inequality

Published on 20 Mar 2026 - 5:34

score 154 · Answer 11 · 2018-01-16 05:07:54

154

Views

Is there an easy way to decide the sign of $\sqrt x \ln (x + 1) - \sqrt {x + 1} \ln x$?

Published on 16 Jan 2018 - 5:07

score 1k · Answer 12 · 2026-03-20 05:40:50

1k

Views

Prove $a^2+b^2+c^2\gt \frac {1}{2018}$ given $\left({3a + 28b + 35c}\right)\left({20a + 23b +33c}\right) = 1$

Published on 20 Mar 2026 - 5:40

score 208 · Answer 13 · 2026-03-23 02:38:03

208

Views

Is it possible to find an upper bound on the moment generating function of $\sqrt{|X|}$, where $X\sim \mathcal{N}(0,1)$?

Published on 23 Mar 2026 - 2:38

score 281 · Answer 14 · 2026-03-21 17:38:37

281

Views

Reverse Riesz-Thorin inequality

Published on 21 Mar 2026 - 17:38

score 188 · Answer 15 · 2026-03-22 10:30:22

188

Views

Prove that $\frac{1}{\sqrt{ab+a+2}}+ \frac{1}{\sqrt{bc+b+2}}+ \frac{1}{\sqrt{ac+c+2}} \leq \frac{3}{2}$

Published on 22 Mar 2026 - 10:30

List Question

Show that $\frac{1}{k}-\ln\left(\frac{k+1}{k}\right)$ is bounded by $\frac{1}{k^2}$

Bounding Probability with Large Variance

How to prove the inequality $\frac{1}{n}+\frac{1}{n+1}+\cdots+\frac{1}{2n-1}\geq \log (2)$?

In resticted domain , Applying the Cauchy-Schwarz's inequality

Mean value theorem for functions from $\mathbb R^n \to \mathbb R^n$

for $x,y,z\ge 0$, $x+y+z=2$, prove $\frac{x}{1+y^2}+\frac{y}{1+z^2}+\frac{z}{1+x^2}\ge\frac{18}{13}$

If $|ax^2+bx+c|\le \frac12$ for all $|x|\le1$, then $|ax^2+bx+c|\le x^2-\frac12$ for all $|x|\ge1$

Interesting inequalities

An algebraic inequality with three components

Solving for the values of x when x is on both sides of a logarithmic inequality

Is there an easy way to decide the sign of $\sqrt x \ln (x + 1) - \sqrt {x + 1} \ln x$?

Prove $a^2+b^2+c^2\gt \frac {1}{2018}$ given $\left({3a + 28b + 35c}\right)\left({20a + 23b +33c}\right) = 1$

Is it possible to find an upper bound on the moment generating function of $\sqrt{|X|}$, where $X\sim \mathcal{N}(0,1)$?

Reverse Riesz-Thorin inequality

Prove that $\frac{1}{\sqrt{ab+a+2}}+ \frac{1}{\sqrt{bc+b+2}}+ \frac{1}{\sqrt{ac+c+2}} \leq \frac{3}{2}$

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