Question

How to show properly that $\left( 1-\sqrt {2}\right) ^{3000} <\left( \frac {1}{10}\right) ^{100}$?

score 182 · Answer 1 · 2018-07-27 09:29:38

182

Views

How to show properly that $\left( 1-\sqrt {2}\right) ^{3000} <\left( \frac {1}{10}\right) ^{100}$?

Published on 27 Jul 2018 - 9:29

score 211 · Answer 2 · 2026-03-31 18:24:46

211

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Is this a (direct) consequence of the Courant-Fischer theorem?

Published on 31 Mar 2026 - 18:24

score 458 · Answer 3 · 2026-03-25 01:34:03

458

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Does Jensen's Inequality hold for complex numbers?

Published on 25 Mar 2026 - 1:34

score 240 · Answer 4 · 2026-02-23 06:16:35

240

Views

constructing a 95% confidence interval - manipulating inequalities

Published on 23 Feb 2026 - 6:16

score 105 · Answer 5 · 2026-03-25 03:07:28

105

Views

Is there a generalization of Araki-Lieb-Thirring inequality for four matrices?

Published on 25 Mar 2026 - 3:07

score 53 · Answer 6 · 2018-07-28 16:54:25

53

Views

How to solve $\log_{\frac{1}{3}}(\frac{3x-1}{x+2})>0$.

Published on 28 Jul 2018 - 16:54

score 121 · Answer 7 · 2026-03-25 20:36:28

121

Views

Is $|\ln(1+t) - t| \leq t^2$ for $|t| \leq \frac{1}{2}$ obvious?

Published on 25 Mar 2026 - 20:36

score 336 · Answer 8 · 2026-04-04 09:29:47

336

Views

Maximum $n$ such that ${n \choose k} \,2^{1 - {k \choose 2}} < 1$ (where $k$ is a constant)

Published on 04 Apr 2026 - 9:29

score 139 · Answer 9 · 2026-03-26 01:25:16

139

Views

Show $\prod_{i=1}^{n}x_i^{\alpha_i} \leq \sum_{i=1}^{n}\alpha_ix_i$ using convexity.

Published on 26 Mar 2026 - 1:25

score 118 · Answer 10 · 2026-03-25 21:00:08

118

Views

Exponential decay of the function

Published on 25 Mar 2026 - 21:00

score 86 · Answer 11 · 2026-03-26 21:08:10

86

Views

Solving quadratic inequality to get the final answer

Published on 26 Mar 2026 - 21:08

score 77 · Answer 12 · 2026-03-27 04:15:21

77

Views

Exchanging max, log and absolute value

Published on 27 Mar 2026 - 4:15

score 74 · Answer 13 · 2026-04-06 18:48:39

74

Views

Strengthening an inequality of exponential series

Published on 06 Apr 2026 - 18:48

score 634 · Answer 14 · 2018-07-30 01:54:57

634

Views

Possible mistake finding the maximum volume of a box with the AM-GM inequality?

Published on 30 Jul 2018 - 1:54

score 129 · Answer 15 · 2026-03-27 03:43:21

129

Views

Prove $\sqrt{x^2+1} + \frac{1}{\sqrt{x^2 +1}}\geq 2$

Published on 27 Mar 2026 - 3:43

List Question

How to show properly that $\left( 1-\sqrt {2}\right) ^{3000} <\left( \frac {1}{10}\right) ^{100}$?

Is this a (direct) consequence of the Courant-Fischer theorem?

Does Jensen's Inequality hold for complex numbers?

constructing a 95% confidence interval - manipulating inequalities

Is there a generalization of Araki-Lieb-Thirring inequality for four matrices?

How to solve $\log_{\frac{1}{3}}(\frac{3x-1}{x+2})>0$.

Is $|\ln(1+t) - t| \leq t^2$ for $|t| \leq \frac{1}{2}$ obvious?

Maximum $n$ such that ${n \choose k} \,2^{1 - {k \choose 2}} < 1$ (where $k$ is a constant)

Show $\prod_{i=1}^{n}x_i^{\alpha_i} \leq \sum_{i=1}^{n}\alpha_ix_i$ using convexity.

Exponential decay of the function

Solving quadratic inequality to get the final answer

Exchanging max, log and absolute value

Strengthening an inequality of exponential series

Possible mistake finding the maximum volume of a box with the AM-GM inequality?

Prove $\sqrt{x^2+1} + \frac{1}{\sqrt{x^2 +1}}\geq 2$

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