Question

Prove $\sum\limits_{cyc}\frac{1}{x^{2017}+ x^{2015}+ 1} \geq 1$ with $x,\,y,\,z>0,\,xyz= 1$

score 166 · Answer 1 · 2026-04-03 10:28:56

166

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Prove $\sum\limits_{cyc}\frac{1}{x^{2017}+ x^{2015}+ 1} \geq 1$ with $x,\,y,\,z>0,\,xyz= 1$

Published on 03 Apr 2026 - 10:28

score 121 · Answer 2 · 2018-06-18 06:00:32

121

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Given $a, b$ so that $0\leqq a, b\leqq 2, a^{-1}+ 2b^{-1}\geqq 2$. Prove that $a^{2}+ b^{2}\leqq 5$ .

Published on 18 Jun 2018 - 6:00

score 164 · Answer 3 · 2026-03-25 14:24:36

164

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Proving $abc(x+y+z)^2\geq a(1-2a)yz+b(1-2b)xz+c(1-2c)xy.$

Published on 25 Mar 2026 - 14:24

score 34 · Answer 4 · 2018-06-18 14:27:27

34

Views

Why is this inequality involving distance metrics true?

Published on 18 Jun 2018 - 14:27

score 471 · Answer 5 · 2026-03-29 07:30:33

471

Views

The "$p$-norm" with $0<p<1$ is quasiconcave for nonnegative vectors

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score 80 · Answer 6 · 2026-04-04 04:59:01

80

Views

Proving that $\left(\frac{1}{10^n}\right)_{n=1}^{\infty}$ is $0.1$-steady

Published on 04 Apr 2026 - 4:59

score 287 · Answer 7 · 2026-03-25 11:10:38

287

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Solve $\sqrt{x^2+10x+9}>|x+2|-5$

Published on 25 Mar 2026 - 11:10

score 65 · Answer 8 · 2018-06-18 20:16:16

65

Views

Where is the mistake in my development?

Published on 18 Jun 2018 - 20:16

score 94 · Answer 9 · 2026-03-25 20:35:49

94

Views

An interesting algebraic inequality involving a square root

Published on 25 Mar 2026 - 20:35

score 117 · Answer 10 · 2018-06-19 01:58:05

117

Views

What is the Cauchy-Schwarz Inequality?

Published on 19 Jun 2018 - 1:58

score 95 · Answer 11 · 2026-03-26 17:46:43

95

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Show that $\sin (x/2)+2\sin (x/4)\leq3\sqrt{3}/2$ for all $x \in [0,2\pi]$

Published on 26 Mar 2026 - 17:46

score 1.1k · Answer 12 · 2018-06-19 09:07:07

1.1k

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How to solve one-sided and two-sided Chebyshev's inequality?

Published on 19 Jun 2018 - 9:07

score 74 · Answer 13 · 2026-03-26 06:32:38

74

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find a set of integers where {$a_i + a_j | 1 \le i \le j \le n$} leave distinct remainders when divided by $n(n+1)/2$

Published on 26 Mar 2026 - 6:32

score 224 · Answer 14 · 2026-03-27 00:09:33

224

Views

A lower bound for the Riemann zeta function

Published on 27 Mar 2026 - 0:09

score 149 · Answer 15 · 2018-06-19 18:10:37

149

Views

Which one is the larger , $10^{30!}$ or $10^{30}!$?

Published on 19 Jun 2018 - 18:10

List Question

Prove $\sum\limits_{cyc}\frac{1}{x^{2017}+ x^{2015}+ 1} \geq 1$ with $x,\,y,\,z>0,\,xyz= 1$

Given $a, b$ so that $0\leqq a, b\leqq 2, a^{-1}+ 2b^{-1}\geqq 2$. Prove that $a^{2}+ b^{2}\leqq 5$ .

Proving $abc(x+y+z)^2\geq a(1-2a)yz+b(1-2b)xz+c(1-2c)xy.$

Why is this inequality involving distance metrics true?

The "$p$-norm" with $0<p<1$ is quasiconcave for nonnegative vectors

Proving that $\left(\frac{1}{10^n}\right)_{n=1}^{\infty}$ is $0.1$-steady

Solve $\sqrt{x^2+10x+9}>|x+2|-5$

Where is the mistake in my development?

An interesting algebraic inequality involving a square root

What is the Cauchy-Schwarz Inequality?

Show that $\sin (x/2)+2\sin (x/4)\leq3\sqrt{3}/2$ for all $x \in [0,2\pi]$

How to solve one-sided and two-sided Chebyshev's inequality?

find a set of integers where {$a_i + a_j | 1 \le i \le j \le n$} leave distinct remainders when divided by $n(n+1)/2$

A lower bound for the Riemann zeta function

Which one is the larger , $10^{30!}$ or $10^{30}!$?

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