Question

Struggle with finding equality condition in an AM-GM inquality problem

score 70 · Answer 1 · 2026-04-11 05:35:25

70

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Struggle with finding equality condition in an AM-GM inquality problem

Published on 11 Apr 2026 - 5:35

score 270 · Answer 2 · 2026-03-25 13:56:21

270

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Lower bound for an integral of a polynomial over an interval of finite length

Published on 25 Mar 2026 - 13:56

score 136 · Answer 3 · 2018-11-06 18:09:32

136

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Show that $ (\frac{n}{3})^{n}<n! < (\frac{n}{2})^{n}$

Published on 06 Nov 2018 - 18:09

score 115 · Answer 4 · 2018-11-06 18:34:01

115

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Show that $2 < (1+\frac{1}{n})^{n}< 3$ without using log or binommial coefficient

Published on 06 Nov 2018 - 18:34

score 59 · Answer 5 · 2026-03-29 19:14:34

Is it possible to show only by induction and without the binomial theorem that $(1+\frac{1}{n+1})^{n+1} - (1+\frac{1}{n})^{n} < 1$?

score 180 · Answer 6 · 2018-11-06 23:43:28

180

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PROOF of $e^x > x^m$, $\forall x>1$

Published on 06 Nov 2018 - 23:43

score 228 · Answer 7 · 2026-04-10 18:36:24

228

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Maximize multivariable integer function

Published on 10 Apr 2026 - 18:36

score 134 · Answer 8 · 2026-04-11 04:07:10

134

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How to prove $|e^{i\theta} - 1| \leq |\theta|$?

Published on 11 Apr 2026 - 4:07

score 230 · Answer 9 · 2026-04-11 00:02:28

230

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Inequality involving Euler-Mascheroni constant

Published on 11 Apr 2026 - 0:02

score 56 · Answer 10 · 2026-03-28 03:26:30

56

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Proving $|Z| \leq \binom{n}{l}/ \binom{m}{l}$

Published on 28 Mar 2026 - 3:26

score 235 · Answer 11 · 2026-04-10 13:22:33

235

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Handling overflow in Matlab with exponential and imaginary error functions

Published on 10 Apr 2026 - 13:22

score 52 · Answer 12 · 2018-11-07 15:50:06

If $a,b\in [0,1], a(1-a) \leq b(1-b)$, is it necessary that $-a\log_2 a - (1-a)\log_2 (1-a) \leq -b\log_2 b - (1-b)\log_2 (1-b)$?

score 68 · Answer 13 · 2026-03-25 07:43:00

68

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Upper bound for the sum $\left|\sum_{i=1}^N x_i\right|^p$

Published on 25 Mar 2026 - 7:43

score 329 · Answer 14 · 2018-11-07 22:35:58

329

Views

Prove that $e^x \cos (\sqrt{x^2+1}) \leq 1$

Published on 07 Nov 2018 - 22:35

score 95 · Answer 15 · 2026-04-01 12:41:47

95

Views

Show that any root $z$ of $z^4+z+3=0$ satisfies $|z|>1$

Published on 01 Apr 2026 - 12:41

List Question

Struggle with finding equality condition in an AM-GM inquality problem

Lower bound for an integral of a polynomial over an interval of finite length

Show that $ (\frac{n}{3})^{n}<n! < (\frac{n}{2})^{n}$

Show that $2 < (1+\frac{1}{n})^{n}< 3$ without using log or binommial coefficient

Is it possible to show only by induction and without the binomial theorem that $(1+\frac{1}{n+1})^{n+1} - (1+\frac{1}{n})^{n} < 1$?

PROOF of $e^x > x^m$, $\forall x>1$

Maximize multivariable integer function

How to prove $|e^{i\theta} - 1| \leq |\theta|$?

Inequality involving Euler-Mascheroni constant

Proving $|Z| \leq \binom{n}{l}/ \binom{m}{l}$

Handling overflow in Matlab with exponential and imaginary error functions

If $a,b\in [0,1], a(1-a) \leq b(1-b)$, is it necessary that $-a\log_2 a - (1-a)\log_2 (1-a) \leq -b\log_2 b - (1-b)\log_2 (1-b)$?

Upper bound for the sum $\left|\sum_{i=1}^N x_i\right|^p$

Prove that $e^x \cos (\sqrt{x^2+1}) \leq 1$

Show that any root $z$ of $z^4+z+3=0$ satisfies $|z|>1$

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