Question

If $q < 0$, prove that the power mean $M_q$ is lesser than the geometric mean $G$

score 33 · Answer 1 · 2020-11-26 11:53:31

33

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If $q < 0$, prove that the power mean $M_q$ is lesser than the geometric mean $G$

Published on 26 Nov 2020 - 11:53

score 34 · Answer 2 · 2026-03-25 23:24:23

34

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

Published on 25 Mar 2026 - 23:24

score 115 · Answer 3 · 2020-11-28 07:26:34

115

Views

Minimizing $\left(a+\frac{1}{a}\right)^{2}+\left(b+\frac{1}{b}\right)^{2}$ over positive reals with $a+b=1$. Why is the minimum not $18$?

Published on 28 Nov 2020 - 7:26

score 91 · Answer 4 · 2020-11-28 16:53:33

91

Views

How to prove the inequality $abc(a+b+c)^2≤(a^3+b^3+c^3)(ab+bc+ca)$?

Published on 28 Nov 2020 - 16:53

score 161 · Answer 5 · 2020-11-28 18:39:34

161

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Minimum value of $\left(\frac{a-b}{b-c}\right)^{4}+\left(\frac{b-c}{c-a}\right)^4+\left(\frac{c-a}{a-b}\right)^{4}$

Published on 28 Nov 2020 - 18:39

score 350 · Answer 6 · 2020-11-30 10:05:07

350

Views

Lagrange Multiplier In Proving AM-GM inequality

Published on 30 Nov 2020 - 10:05

score 91 · Answer 7 · 2020-12-02 15:15:37

91

Views

Inequality using AM GM

Published on 02 Dec 2020 - 15:15

score 201 · Answer 8 · 2026-03-25 21:48:43

201

Views

Prove the inequality $4(a+b+c)^3\ge 27(a^2b+b^2c+c^2a)$

Published on 25 Mar 2026 - 21:48

score 69 · Answer 9 · 2020-12-05 11:07:27

69

Views

Inequality form olympiad

Published on 05 Dec 2020 - 11:07

score 349 · Answer 10 · 2026-03-25 23:23:29

349

Views

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 25 Mar 2026 - 23:23

score 84 · Answer 11 · 2020-12-13 20:57:37

Let a,b and c be the three sides of a triangle. Show that $\dfrac 1a+\dfrac 1b+\dfrac 1c\le \dfrac 1{a+b-c}+\dfrac 1{a-b+c}+\dfrac 1{-a+b+c}.$

score 70 · Answer 12 · 2020-12-15 22:02:43

70

Views

Prove the following inequality using the AM-GM Mean

Published on 15 Dec 2020 - 22:02

score 63 · Answer 13 · 2020-12-18 15:27:16

63

Views

Does the inequality of arithmetic and geometric means hold in the limit?

Published on 18 Dec 2020 - 15:27

score 73 · Answer 14 · 2026-03-25 23:24:23

73

Views

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 25 Mar 2026 - 23:24

score 141 · Answer 15 · 2020-12-24 12:09:17

141

Views

Prove that $\frac1{1+a}+\frac1{1+b}+\frac1{1+c}\leq\frac14(a+b+c+3)$ if $abc=1$

Published on 24 Dec 2020 - 12:09

List Question

If $q < 0$, prove that the power mean $M_q$ is lesser than the geometric mean $G$

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

Minimizing $\left(a+\frac{1}{a}\right)^{2}+\left(b+\frac{1}{b}\right)^{2}$ over positive reals with $a+b=1$. Why is the minimum not $18$?

How to prove the inequality $abc(a+b+c)^2≤(a^3+b^3+c^3)(ab+bc+ca)$?

Minimum value of $\left(\frac{a-b}{b-c}\right)^{4}+\left(\frac{b-c}{c-a}\right)^4+\left(\frac{c-a}{a-b}\right)^{4}$

Lagrange Multiplier In Proving AM-GM inequality

Inequality using AM GM

Prove the inequality $4(a+b+c)^3\ge 27(a^2b+b^2c+c^2a)$

Inequality form olympiad

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

Let a,b and c be the three sides of a triangle. Show that $\dfrac 1a+\dfrac 1b+\dfrac 1c\le \dfrac 1{a+b-c}+\dfrac 1{a-b+c}+\dfrac 1{-a+b+c}.$

Prove the following inequality using the AM-GM Mean

Does the inequality of arithmetic and geometric means hold in the limit?

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

Prove that $\frac1{1+a}+\frac1{1+b}+\frac1{1+c}\leq\frac14(a+b+c+3)$ if $abc=1$

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