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Question about an inequality about geometric mean

score 39 · Answer 1 · 2026-04-07 21:31:33

39

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Question about an inequality about geometric mean

Published on 07 Apr 2026 - 21:31

score 293 · Answer 2 · 2026-04-15 22:32:21

293

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Prove that $a^2+b^2+c^2\geqslant\frac{1}{3}$ given that $a\gt0, b\gt0, c\gt0$ and $a+b+c=1$, using existing AM GM inequality

Published on 15 Apr 2026 - 22:32

score 371 · Answer 3 · 2026-04-17 13:44:43

371

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Prove that inequality $\sqrt{2\sqrt{4\sqrt{8....\sqrt{2^n}}}} \leqslant n+1$

Published on 17 Apr 2026 - 13:44

score 50 · Answer 4 · 2026-04-09 01:13:58

50

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Rewrite conditional distribution that is an inequality as a function

Published on 09 Apr 2026 - 1:13

score 285 · Answer 5 · 2026-04-10 22:21:04

285

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Understanding a proof from the APMO 1998 on inequalities.

Published on 10 Apr 2026 - 22:21

score 271 · Answer 6 · 2026-04-16 15:13:59

271

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For three positive numbers verifying $xyz=2+x+y+z$, is there an upper bound on $x+y+z$? And, if so, which is that?

Published on 16 Apr 2026 - 15:13

score 57 · Answer 7 · 2026-03-25 06:08:29

57

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Norm Inequality for 1 Dimensional Sobolev Space

Published on 25 Mar 2026 - 6:08

score 101 · Answer 8 · 2026-04-13 20:01:49

101

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An inequality question about $x\ln x+x^2$.

Published on 13 Apr 2026 - 20:01

score 66 · Answer 9 · 2026-04-17 00:53:42

66

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Using Jensen's inequality prove: (1) $~n!<n^n<(n!)^2$ for $n>1$ and (2) $~e^n\geqslant \frac{n^n}{n!}.$

Published on 17 Apr 2026 - 0:53

score 57 · Answer 10 · 2026-04-10 10:17:33

57

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Comparing inequalities using convexity of the function

Published on 10 Apr 2026 - 10:17

score 276 · Answer 11 · 2026-03-25 06:34:58

276

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find the maximum and minimum of $\sum_{i=1}^{n} (10x^3_{i}-9x^5_{i})$

Published on 25 Mar 2026 - 6:34

score 787 · Answer 12 · 2026-03-25 07:46:00

787

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If $a$, $b$ and $c$ are sides of a triangle, then prove that $a^\text{2}(b+c-a) + b^\text{2}(c+a-b) + c^\text{2}(a+b-c)$ $\leqslant$ $3abc$

Published on 25 Mar 2026 - 7:46

score 151 · Answer 13 · 2026-04-11 11:36:27

151

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Positive definiteness and eigenvalue ellipses

Published on 11 Apr 2026 - 11:36

score 176 · Answer 14 · 2026-04-17 08:34:42

176

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How to prove that $\left(\ln(\ln(x)) \right)^2 \lt \ln(x)$

Published on 17 Apr 2026 - 8:34

score 98 · Answer 15 · 2026-04-14 01:48:21

98

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Matrix and determinant inequality

Published on 14 Apr 2026 - 1:48

List Question

Question about an inequality about geometric mean

Prove that $a^2+b^2+c^2\geqslant\frac{1}{3}$ given that $a\gt0, b\gt0, c\gt0$ and $a+b+c=1$, using existing AM GM inequality

Prove that inequality $\sqrt{2\sqrt{4\sqrt{8....\sqrt{2^n}}}} \leqslant n+1$

Rewrite conditional distribution that is an inequality as a function

Understanding a proof from the APMO 1998 on inequalities.

For three positive numbers verifying $xyz=2+x+y+z$, is there an upper bound on $x+y+z$? And, if so, which is that?

Norm Inequality for 1 Dimensional Sobolev Space

An inequality question about $x\ln x+x^2$.

Using Jensen's inequality prove: (1) $~n!<n^n<(n!)^2$ for $n>1$ and (2) $~e^n\geqslant \frac{n^n}{n!}.$

Comparing inequalities using convexity of the function

find the maximum and minimum of $\sum_{i=1}^{n} (10x^3_{i}-9x^5_{i})$

If $a$, $b$ and $c$ are sides of a triangle, then prove that $a^\text{2}(b+c-a) + b^\text{2}(c+a-b) + c^\text{2}(a+b-c)$ $\leqslant$ $3abc$

Positive definiteness and eigenvalue ellipses

How to prove that $\left(\ln(\ln(x)) \right)^2 \lt \ln(x)$

Matrix and determinant inequality

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