Question

Natural numbers inequality $na^{n-1}b\leq(n-1)a^n+b^n$ by induction

score 119 · Answer 1 · 2026-03-25 13:56:20

119

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Natural numbers inequality $na^{n-1}b\leq(n-1)a^n+b^n$ by induction

Published on 25 Mar 2026 - 13:56

score 56 · Answer 2 · 2026-03-25 13:54:40

56

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How many Steiner Symmetrizations does it take to make an arbitrary set convex?

Published on 25 Mar 2026 - 13:54

score 177 · Answer 3 · 2026-03-25 13:55:11

177

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One of my old inequality (very sharp)

Published on 25 Mar 2026 - 13:55

score 121 · Answer 4 · 2026-04-05 18:51:12

121

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Inequality from Israel TST

Published on 05 Apr 2026 - 18:51

score 153 · Answer 5 · 2026-05-10 16:35:49

153

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For $a,b,c\in\left[\frac{1}{\sqrt{6}}, 6\right]$: $\sum_{cyc}\frac{4}{a+3b}\geq \sum_{cyc}\frac{3}{a+2b}$

Published on 10 May 2026 - 16:35

score 71 · Answer 6 · 2026-03-25 13:55:08

71

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Where is the flaw in this using Rearrangement Inequality?

Published on 25 Mar 2026 - 13:55

score 79 · Answer 7 · 2026-03-25 13:56:25

79

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$ \frac{a^{2}}{a+2 b^{3}}+\frac{b^{2}}{b+2 c^{3}}+\frac{c^{2}}{c+2 a^{3}} \geq 1 $

Published on 25 Mar 2026 - 13:56

score 140 · Answer 8 · 2026-03-25 13:56:19

140

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If $a+b+c=3$ Prove that $a^{2}+b^{2}+c^{2}\geq\frac{2+a}{2+b}+\frac{2+b}{2+c}+\frac{2+c}{2+a}$

Published on 25 Mar 2026 - 13:56

score 74 · Answer 9 · 2026-03-25 13:59:39

74

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Proving an inequality regarding increasing or decreasing sequences

Published on 25 Mar 2026 - 13:59

score 157 · Answer 10 · 2026-03-25 13:56:59

157

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If $a,b,c>0$ and $a+b+c=1$, then prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\le 3+2\cdot\frac{a^3+b^3+c^3}{abc}$.

Published on 25 Mar 2026 - 13:56

score 715 · Answer 11 · 2026-03-25 13:55:34

715

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If $a, b, c\in\mathbb R^+, $ then prove that $a^3b+b^3c+c^3a\ge abc(a+b+c) .$

Published on 25 Mar 2026 - 13:55

score 59 · Answer 12 · 2026-03-25 13:52:59

59

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Maximum value of a parameter in a cyclic inequality?

Published on 25 Mar 2026 - 13:52

score 87 · Answer 13 · 2026-05-10 17:39:19

87

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If $abc=1$, then how do you prove $\frac{b-1}{bc+1}+\frac{c-1}{ac+1}+\frac{a-1}{ab+1} \geq 0$?

Published on 10 May 2026 - 17:39

score 147 · Answer 14 · 2026-03-25 13:57:08

147

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Prove: $\sqrt{\frac{bc}{a(3b+a)}} + \sqrt{\frac{ac}{b(3c+b)}} + \sqrt{\frac{ab}{c(3a+c)}} \ge \frac{3}{2}$.

Published on 25 Mar 2026 - 13:57

score 81 · Answer 15 · 2026-03-25 11:16:41

81

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on possible generalisations of $1\le\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}\le 2$

Published on 25 Mar 2026 - 11:16

List Question

Natural numbers inequality $na^{n-1}b\leq(n-1)a^n+b^n$ by induction

How many Steiner Symmetrizations does it take to make an arbitrary set convex?

One of my old inequality (very sharp)

Inequality from Israel TST

For $a,b,c\in\left[\frac{1}{\sqrt{6}}, 6\right]$: $\sum_{cyc}\frac{4}{a+3b}\geq \sum_{cyc}\frac{3}{a+2b}$

Where is the flaw in this using Rearrangement Inequality?

$ \frac{a^{2}}{a+2 b^{3}}+\frac{b^{2}}{b+2 c^{3}}+\frac{c^{2}}{c+2 a^{3}} \geq 1 $

If $a+b+c=3$ Prove that $a^{2}+b^{2}+c^{2}\geq\frac{2+a}{2+b}+\frac{2+b}{2+c}+\frac{2+c}{2+a}$

Proving an inequality regarding increasing or decreasing sequences

If $a,b,c>0$ and $a+b+c=1$, then prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\le 3+2\cdot\frac{a^3+b^3+c^3}{abc}$.

If $a, b, c\in\mathbb R^+, $ then prove that $a^3b+b^3c+c^3a\ge abc(a+b+c) .$

Maximum value of a parameter in a cyclic inequality?

If $abc=1$, then how do you prove $\frac{b-1}{bc+1}+\frac{c-1}{ac+1}+\frac{a-1}{ab+1} \geq 0$?

Prove: $\sqrt{\frac{bc}{a(3b+a)}} + \sqrt{\frac{ac}{b(3c+b)}} + \sqrt{\frac{ab}{c(3a+c)}} \ge \frac{3}{2}$.

on possible generalisations of $1\le\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}\le 2$

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