Question

Proof verification of $\left(1+{1\over n}\right)^n > e^{1-1/n}$ for all $n\in\Bbb N$.

score 156 · Answer 1 · 2026-04-16 00:27:38

156

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Proof verification of $\left(1+{1\over n}\right)^n > e^{1-1/n}$ for all $n\in\Bbb N$.

Published on 16 Apr 2026 - 0:27

score 83 · Answer 2 · 2026-04-15 05:55:11

83

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How to show $(1-x)^n<\frac{1}{1+nx}$?

Published on 15 Apr 2026 - 5:55

score 108 · Answer 3 · 2026-04-15 21:12:52

108

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Prove that the functional is non-negative for $x_i\geq 0$

Published on 15 Apr 2026 - 21:12

score 36 · Answer 4 · 2026-04-12 00:41:37

36

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inequality of variables without knowing their sign

Published on 12 Apr 2026 - 0:41

score 214 · Answer 5 · 2026-04-09 05:33:19

214

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Is this a valid conclusion from Chebyshev's first and second function

Published on 09 Apr 2026 - 5:33

score 82 · Answer 6 · 2026-04-14 11:05:38

82

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Prove the inequality $\sum_{cyc} {{a+abc} \over {1+ab+abcd}} \ge {{10} \over {3}}$ with Cauchy-Schwarz

Published on 14 Apr 2026 - 11:05

score 210 · Answer 7 · 2026-04-15 22:34:01

210

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Inequality. $\sum_{cyc}(\frac{1}{a+b+\sqrt{2a+2c}})^3 \le \frac{8}{9}$

Published on 15 Apr 2026 - 22:34

score 71 · Answer 8 · 2026-04-15 16:50:26

71

Views

Regarding $x < y \Rightarrow x^n < y^n$ proof rigor.

Published on 15 Apr 2026 - 16:50

score 81 · Answer 9 · 2026-04-16 00:11:58

81

Views

Show that $x^2 + 2y^2 + z^2 - 2yz > 0$.

Published on 16 Apr 2026 - 0:11

score 123 · Answer 10 · 2026-04-17 13:42:16

123

Views

Prove or disprove the inequality $ -x\ln (x)\leq \ln(1-x)(\ln (x) + 1 - x)$

Published on 17 Apr 2026 - 13:42

score 418 · Answer 11 · 2026-04-16 15:45:06

418

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Excercise 2.4 in Jurgen Jost's PDE "Harnack's inequality" for harmonic functions defined on a ball

Published on 16 Apr 2026 - 15:45

score 368 · Answer 12 · 2026-04-12 01:46:13

368

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Inequality between Frobenius norm and L2 Norm

Published on 12 Apr 2026 - 1:46

score 55 · Answer 13 · 2026-04-16 15:14:41

55

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Proving Inequalities Involving Summations and Sq. Roots

Published on 16 Apr 2026 - 15:14

score 111 · Answer 14 · 2026-04-15 09:17:39

111

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Inequality problem: with $x,y,z>0$, show that $\frac{x^5}{y^3}+\frac{y^5}{z^3}+\frac{z^5}{x^3}\geq x^2+y^2+z^2$

Published on 15 Apr 2026 - 9:17

score 278 · Answer 15 · 2026-04-14 15:39:00

278

Views

Real Analysis Inequality Proof Involving Reals and Rationals $0 < |r - q| < \varepsilon$

Published on 14 Apr 2026 - 15:39

List Question

Proof verification of $\left(1+{1\over n}\right)^n > e^{1-1/n}$ for all $n\in\Bbb N$.

How to show $(1-x)^n<\frac{1}{1+nx}$?

Prove that the functional is non-negative for $x_i\geq 0$

inequality of variables without knowing their sign

Is this a valid conclusion from Chebyshev's first and second function

Prove the inequality $\sum_{cyc} {{a+abc} \over {1+ab+abcd}} \ge {{10} \over {3}}$ with Cauchy-Schwarz

Inequality. $\sum_{cyc}(\frac{1}{a+b+\sqrt{2a+2c}})^3 \le \frac{8}{9}$

Regarding $x < y \Rightarrow x^n < y^n$ proof rigor.

Show that $x^2 + 2y^2 + z^2 - 2yz > 0$.

Prove or disprove the inequality $ -x\ln (x)\leq \ln(1-x)(\ln (x) + 1 - x)$

Excercise 2.4 in Jurgen Jost's PDE "Harnack's inequality" for harmonic functions defined on a ball

Inequality between Frobenius norm and L2 Norm

Proving Inequalities Involving Summations and Sq. Roots

Inequality problem: with $x,y,z>0$, show that $\frac{x^5}{y^3}+\frac{y^5}{z^3}+\frac{z^5}{x^3}\geq x^2+y^2+z^2$

Real Analysis Inequality Proof Involving Reals and Rationals $0 < |r - q| < \varepsilon$

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