List questions from rearrangement-inequality

Published on 06 Sep 2020 - 7:01

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How and when to assume WLOG correctly?

Published on 10 Sep 2020 - 8:44

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Rearrange 2nd sequence so that no two elements at same index are equal.

Published on 25 Mar 2026 - 3:30

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Homogenization, what it is in inequalities and how to utilize it to its fullest.

Published on 22 Sep 2020 - 14:24

112

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Why this inequality is correct

Published on 10 Oct 2020 - 23:55

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Proving a cyclic inequality

Published on 18 Oct 2020 - 8:49

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Verification to solution an inequality and proving another.

Published on 23 Oct 2020 - 11:45

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$\frac{b^2-a^2}{c+a} + \frac{c^2-b^2}{a+b} + \frac{a^2-c^2}{b+c} \ge 0$ Proof

Published on 29 Oct 2020 - 20:10

121

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prove $\sum_\text{cyc}\frac{a+2}{b+2}\le \sum_\text{cyc}\frac{a}{b}$

Published on 31 Oct 2020 - 16:48

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Convergence/divergence of sum of finite products of functions of reciprocals of natural numbers

Published on 27 Nov 2020 - 23:46

348

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Proving $ \sum_{cyc} \frac{1}{a^6 + b^6 + 3c^3 + 4} \leq \frac{3}{3 + 2(\sqrt{ab} + \sqrt{bc} + \sqrt{ca})}$

Published on 09 Dec 2020 - 14:04

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If $x,y,z>0$, $n,m\in N$, $n\ge m$ prove:$\frac{x^n}{(y+z)^m}+\frac{y^n}{(z+x)^m}+\frac{z^n}{(x+y)^m}\ge \frac{1}{2^m}(x^{n-m}+y^{n-m}+z^{n-m})$

Published on 22 Dec 2020 - 13:14

259

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Inequality $a^2b(a-b) + b^2c(b-c) + c^2a(c-a) \geq 0$

Published on 01 Feb 2021 - 15:54

106

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With $n> 3,$ prove that $a_{1}+ a_{2}+ a_{3}\geq 100$ by using Karamata's inequality

Published on 23 Feb 2026 - 19:00

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Given 4 numbers $a, b, c, d> 0,$ show $16\max\limits_{\bigcirc}\left \{ a^{3}+ 3bcd \right \}\!\geq\!\left ( a+ b+ c+ d \right )^{3}$

Published on 23 Feb 2026 - 18:59

List Question

One question and a challenge regarding Collatz looping proof.

How and when to assume WLOG correctly?

Rearrange 2nd sequence so that no two elements at same index are equal.

Homogenization, what it is in inequalities and how to utilize it to its fullest.

Why this inequality is correct

Proving a cyclic inequality

Verification to solution an inequality and proving another.

$\frac{b^2-a^2}{c+a} + \frac{c^2-b^2}{a+b} + \frac{a^2-c^2}{b+c} \ge 0$ Proof

prove $\sum_\text{cyc}\frac{a+2}{b+2}\le \sum_\text{cyc}\frac{a}{b}$

Convergence/divergence of sum of finite products of functions of reciprocals of natural numbers

Proving $ \sum_{cyc} \frac{1}{a^6 + b^6 + 3c^3 + 4} \leq \frac{3}{3 + 2(\sqrt{ab} + \sqrt{bc} + \sqrt{ca})}$

If $x,y,z>0$, $n,m\in N$, $n\ge m$ prove:$\frac{x^n}{(y+z)^m}+\frac{y^n}{(z+x)^m}+\frac{z^n}{(x+y)^m}\ge \frac{1}{2^m}(x^{n-m}+y^{n-m}+z^{n-m})$

Inequality $a^2b(a-b) + b^2c(b-c) + c^2a(c-a) \geq 0$

With $n> 3,$ prove that $a_{1}+ a_{2}+ a_{3}\geq 100$ by using Karamata's inequality

Given 4 numbers $a, b, c, d> 0,$ show $16\max\limits_{\bigcirc}\left \{ a^{3}+ 3bcd \right \}\!\geq\!\left ( a+ b+ c+ d \right )^{3}$

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