Question

Inequality with absolute value with unknowns

score 46 · Answer 1 · 2026-03-25 04:35:13

46

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Inequality with absolute value with unknowns

Published on 25 Mar 2026 - 4:35

score 458 · Answer 2 · 2026-03-26 17:31:37

458

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Show that $\cos(x) \le e^{-x^2/2}$ for $0 \le x \lt \pi/2$.

Published on 26 Mar 2026 - 17:31

score 167 · Answer 3 · 2018-05-07 02:29:09

167

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$x_1=1,x_n=x_{n+1}+\ln (1+x_{n+1})$, prove $x_n\leq\frac{1}{2^{n-2}}$.

Published on 07 May 2018 - 2:29

score 56 · Answer 4 · 2018-05-07 03:27:11

56

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Positive sequence $\{a_n\}$, $a_{n+1}=-\sqrt{a_n}+1, a_1\in{(\frac12,1)}$. Prove $a_{2n+1}+a_{2n+2}<a_{2n-1}+a_{2n}$.

Published on 07 May 2018 - 3:27

score 44 · Answer 5 · 2018-05-07 08:17:19

44

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Proving inequality for derivative relationship

Published on 07 May 2018 - 8:17

score 145 · Answer 6 · 2018-05-07 11:02:47

145

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$f'(x) \geq x$, then $f(x) \leq f(0) + \frac12 x^2 ,$ when $x \leq 0$.

Published on 07 May 2018 - 11:02

score 32 · Answer 7 · 2026-03-26 04:52:17

32

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If $\frac{a}{c}<\frac{a'}{c'}<\frac{b}{d}$ and $bc-ad=1$, Then $a' = \lambda_1 a + \lambda_2 b$ and $c' = \lambda_1 c + \lambda_2 d$

Published on 26 Mar 2026 - 4:52

score 153 · Answer 8 · 2018-05-07 16:29:03

153

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Proving that the following inequality is true for all $n$.

Published on 07 May 2018 - 16:29

score 93 · Answer 9 · 2026-03-25 04:37:28

93

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Minimizer of parametrized convex function

Published on 25 Mar 2026 - 4:37

score 108 · Answer 10 · 2026-03-25 19:11:59

108

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If AM-GM holds for any $2^n$ positive real numbers, show that AM-GM holds for any number of positive real numbers.

Published on 25 Mar 2026 - 19:11

score 246 · Answer 11 · 2018-05-08 06:53:09

246

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Applying Gronwall inequality for $\frac{d}{dt}\|u(t)\|_{L^{q}}^q \leq f(t) + C\|u(t)\|_{L^{q}}^{q-2}$

Published on 08 May 2018 - 6:53

score 545 · Answer 12 · 2026-03-25 12:25:30

545

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For $n \ge 4$, does it follow that ${{3n} \choose {n}} > 4^n$

Published on 25 Mar 2026 - 12:25

score 56 · Answer 13 · 2018-05-08 11:23:01

56

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Intuitive probability inequality

Published on 08 May 2018 - 11:23

score 47 · Answer 14 · 2018-05-08 15:34:51

47

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Show $\frac{d(a,c)}{1+d(a,c)}\leq \frac{d(a, b)+d(b,c)}{1+d(a, b)+d(b,c)}$

Published on 08 May 2018 - 15:34

score 57 · Answer 15 · 2026-03-30 23:15:33

57

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Trying to solve this inequation $x\in [0, 2\pi]$: $\log_{\cos{x}}(1+2\cos{x})+\log_{\cos{x}}(1+\cos{x})>1$

Published on 30 Mar 2026 - 23:15

List Question

Inequality with absolute value with unknowns

Show that $\cos(x) \le e^{-x^2/2}$ for $0 \le x \lt \pi/2$.

$x_1=1,x_n=x_{n+1}+\ln (1+x_{n+1})$, prove $x_n\leq\frac{1}{2^{n-2}}$.

Positive sequence $\{a_n\}$, $a_{n+1}=-\sqrt{a_n}+1, a_1\in{(\frac12,1)}$. Prove $a_{2n+1}+a_{2n+2}<a_{2n-1}+a_{2n}$.

Proving inequality for derivative relationship

$f'(x) \geq x$, then $f(x) \leq f(0) + \frac12 x^2 ,$ when $x \leq 0$.

If $\frac{a}{c}<\frac{a'}{c'}<\frac{b}{d}$ and $bc-ad=1$, Then $a' = \lambda_1 a + \lambda_2 b$ and $c' = \lambda_1 c + \lambda_2 d$

Proving that the following inequality is true for all $n$.

Minimizer of parametrized convex function

If AM-GM holds for any $2^n$ positive real numbers, show that AM-GM holds for any number of positive real numbers.

Applying Gronwall inequality for $\frac{d}{dt}\|u(t)\|_{L^{q}}^q \leq f(t) + C\|u(t)\|_{L^{q}}^{q-2}$

For $n \ge 4$, does it follow that ${{3n} \choose {n}} > 4^n$

Intuitive probability inequality

Show $\frac{d(a,c)}{1+d(a,c)}\leq \frac{d(a, b)+d(b,c)}{1+d(a, b)+d(b,c)}$

Trying to solve this inequation $x\in [0, 2\pi]$: $\log_{\cos{x}}(1+2\cos{x})+\log_{\cos{x}}(1+\cos{x})>1$

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