Question

Using the Arithmetic Mean-Geometric Mean Inequality to prove convergence of a series

score 223 · Answer 1 · 2020-06-25 17:26:16

223

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Using the Arithmetic Mean-Geometric Mean Inequality to prove convergence of a series

Published on 25 Jun 2020 - 17:26

score 121 · Answer 2 · 2020-07-01 07:08:33

121

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Number of Real Solutions of $\frac{7^{1+\cos(\pi x)}}{3}+3^{x^2-2}+9^{\frac{1}{2}-|x|}=1$

Published on 01 Jul 2020 - 7:08

score 198 · Answer 3 · 2020-07-02 15:36:20

198

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For $a,b,c>0$ prove that $abc(a+b+c) \le a^3 b + b^3 c + c^3 a$

Published on 02 Jul 2020 - 15:36

score 254 · Answer 4 · 2026-03-28 03:03:07

254

Views

Proving $(a+b+c)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)+3\ge 4\cdot \frac{a+b+c}{\sqrt[3]{abc}}$ for positive $a$, $b$, $c$

Published on 28 Mar 2026 - 3:03

score 60 · Answer 5 · 2026-03-25 17:38:35

60

Views

Proving that an inequality holds

Published on 25 Mar 2026 - 17:38

score 123 · Answer 6 · 2026-03-25 06:07:05

123

Views

Given positive real numbers $a$, $b$, $c$, $d$, $e$ with $\sum_{\text{cyc}}\,\frac{1}{4+a}=1$, prove that $\sum_{\text{cyc}}\,\frac{a}{4+a^2}\le1$.

Published on 25 Mar 2026 - 6:07

score 135 · Answer 7 · 2020-07-07 22:52:10

135

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Use the arithmetic mean-geometric mean inequality to establish that $-x < n < m$ implies $(1+x/n)^{n} \leq (1 + x/m)^{m}$

Published on 07 Jul 2020 - 22:52

score 80 · Answer 8 · 2020-07-08 06:01:41

80

Views

Problem with $AM>GM>HM$ inequality

Published on 08 Jul 2020 - 6:01

score 108 · Answer 9 · 2026-03-25 20:42:24

108

Views

Is the inequality true for all $n\geq 2$?

Published on 25 Mar 2026 - 20:42

score 298 · Answer 10 · 2020-07-12 10:36:50

298

Views

Prove inequality $\tan(x) \arctan(x) \geqslant x^2$

Published on 12 Jul 2020 - 10:36

score 91 · Answer 11 · 2020-07-13 05:19:11

91

Views

Problem with proving inequalities

Published on 13 Jul 2020 - 5:19

score 65 · Answer 12 · 2026-03-25 02:57:37

65

Views

Inqualitiy with exponent

Published on 25 Mar 2026 - 2:57

score 209 · Answer 13 · 2026-02-23 04:43:04

209

Views

How to prove that if $x>0$ and $y>0$, then $\sqrt{x}+\sqrt{y}>\sqrt{x+y}$, using the relation of arithmetic and geometric means?

Published on 23 Feb 2026 - 4:43

score 240 · Answer 14 · 2026-03-28 01:11:48

240

Views

AM/GM inequalities

Published on 28 Mar 2026 - 1:11

score 171 · Answer 15 · 2020-07-18 11:31:27

171

Views

Let $a_2,a_3,\cdots,a_n$ be positive real numbers and $s=a_2+a_3+\cdots+a_n$. Show that $\sum\limits_{k=2}^na_k^{1-\frac{1}{k}}<s+2\sqrt{s}$

Published on 18 Jul 2020 - 11:31

List Question

Using the Arithmetic Mean-Geometric Mean Inequality to prove convergence of a series

Number of Real Solutions of $\frac{7^{1+\cos(\pi x)}}{3}+3^{x^2-2}+9^{\frac{1}{2}-|x|}=1$

For $a,b,c>0$ prove that $abc(a+b+c) \le a^3 b + b^3 c + c^3 a$

Proving $(a+b+c)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)+3\ge 4\cdot \frac{a+b+c}{\sqrt[3]{abc}}$ for positive $a$, $b$, $c$

Proving that an inequality holds

Given positive real numbers $a$, $b$, $c$, $d$, $e$ with $\sum_{\text{cyc}}\,\frac{1}{4+a}=1$, prove that $\sum_{\text{cyc}}\,\frac{a}{4+a^2}\le1$.

Use the arithmetic mean-geometric mean inequality to establish that $-x < n < m$ implies $(1+x/n)^{n} \leq (1 + x/m)^{m}$

Problem with $AM>GM>HM$ inequality

Is the inequality true for all $n\geq 2$?

Prove inequality $\tan(x) \arctan(x) \geqslant x^2$

Problem with proving inequalities

Inqualitiy with exponent

How to prove that if $x>0$ and $y>0$, then $\sqrt{x}+\sqrt{y}>\sqrt{x+y}$, using the relation of arithmetic and geometric means?

AM/GM inequalities

Let $a_2,a_3,\cdots,a_n$ be positive real numbers and $s=a_2+a_3+\cdots+a_n$. Show that $\sum\limits_{k=2}^na_k^{1-\frac{1}{k}}<s+2\sqrt{s}$

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