Question

Prove Combinatoric Inequality

score 78 · Answer 1 · 2026-03-25 01:14:23

78

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Prove Combinatoric Inequality

Published on 25 Mar 2026 - 1:14

score 109 · Answer 2 · 2026-03-26 02:56:12

109

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Prove that $\sum\limits_{n=1}^{2000} \frac {1}{n^3+3n^2+2n}\lt \frac {1}{4}$

Published on 26 Mar 2026 - 2:56

score 184 · Answer 3 · 2018-02-12 10:32:42

184

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How to prove that $\int_{0}^{\pi}\left|{\sin{nx}\over x}\right|\,\mathrm dx\ge{2\over\pi} \sum\limits_{k = 1}^n \frac1k$

Published on 12 Feb 2018 - 10:32

score 170 · Answer 4 · 2026-03-20 05:01:42

170

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What is the infimal norm of a matrix in a conjugacy class?

Published on 20 Mar 2026 - 5:01

score 88 · Answer 5 · 2018-02-12 16:26:56

88

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A Minkowski like inequality for symmetric sums

Published on 12 Feb 2018 - 16:26

score 73 · Answer 6 · 2026-03-25 04:25:15

73

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What's the reason behind $e^{tx} \leq \frac{b-x}{b-a}e^{ta}+\frac{x-a}{b-a}e^{tb}$?

Published on 25 Mar 2026 - 4:25

score 39 · Answer 7 · 2018-02-12 17:53:39

39

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Proving an inequality using relationships between means

Published on 12 Feb 2018 - 17:53

score 122 · Answer 8 · 2026-03-24 22:01:29

122

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Use Triangle Inequalities to Prove an Inequality

Published on 24 Mar 2026 - 22:01

score 353 · Answer 9 · 2026-03-23 01:33:23

353

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Prove that $(x-y)(y-z)(z-x) \leq \frac{1}{\sqrt{2}}$

Published on 23 Mar 2026 - 1:33

score 126 · Answer 10 · 2026-03-25 05:06:47

126

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Trigonometric Inequality $\sin{A}+\sin{B}-\cos{C}\le\frac32$

Published on 25 Mar 2026 - 5:06

score 84 · Answer 11 · 2026-03-25 06:07:12

84

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Proving $ \frac {(a+b)^2 }{\sqrt{(a+b)^2 +1}} < 2 \left( \frac {a^2 }{\sqrt{ a^2 +1}} + \frac{b^2 } {\sqrt{ b^2 +1 }} \right) $

Published on 25 Mar 2026 - 6:07

score 51 · Answer 12 · 2018-02-13 13:24:42

51

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Inequality with $a\le b\le c$ and $a+b+c=1$

Published on 13 Feb 2018 - 13:24

score 581 · Answer 13 · 2026-03-27 17:06:01

581

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How to prove that $x^2yz+xy^2z+xyz^2 \leq \frac{1}{3}$ where $x^2+y^2+z^2 = 1$ and $x,y,z >0$?

Published on 27 Mar 2026 - 17:06

score 54 · Answer 14 · 2018-02-13 15:45:27

54

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True or not $\int_{-\infty}^{\infty}\lvert\log\sqrt{f(x)}\rvert dx\le\frac12\int\limits_{-\infty}^{\infty}\lvert\log\left(f(x)\right)\rvert dx$

Published on 13 Feb 2018 - 15:45

score 2.2k · Answer 15 · 2018-02-13 19:28:21

2.2k

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Is the product of numbers always less than or equal to the sum of squares?

Published on 13 Feb 2018 - 19:28

List Question

Prove Combinatoric Inequality

Prove that $\sum\limits_{n=1}^{2000} \frac {1}{n^3+3n^2+2n}\lt \frac {1}{4}$

How to prove that $\int_{0}^{\pi}\left|{\sin{nx}\over x}\right|\,\mathrm dx\ge{2\over\pi} \sum\limits_{k = 1}^n \frac1k$

What is the infimal norm of a matrix in a conjugacy class?

A Minkowski like inequality for symmetric sums

What's the reason behind $e^{tx} \leq \frac{b-x}{b-a}e^{ta}+\frac{x-a}{b-a}e^{tb}$?

Proving an inequality using relationships between means

Use Triangle Inequalities to Prove an Inequality

Prove that $(x-y)(y-z)(z-x) \leq \frac{1}{\sqrt{2}}$

Trigonometric Inequality $\sin{A}+\sin{B}-\cos{C}\le\frac32$

Proving $ \frac {(a+b)^2 }{\sqrt{(a+b)^2 +1}} < 2 \left( \frac {a^2 }{\sqrt{ a^2 +1}} + \frac{b^2 } {\sqrt{ b^2 +1 }} \right) $

Inequality with $a\le b\le c$ and $a+b+c=1$

How to prove that $x^2yz+xy^2z+xyz^2 \leq \frac{1}{3}$ where $x^2+y^2+z^2 = 1$ and $x,y,z >0$?

True or not $\int_{-\infty}^{\infty}\lvert\log\sqrt{f(x)}\rvert dx\le\frac12\int\limits_{-\infty}^{\infty}\lvert\log\left(f(x)\right)\rvert dx$

Is the product of numbers always less than or equal to the sum of squares?

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