Question

Prove that $\forall n \in \Bbb{N}, 1 <n, \left( 1 + \frac{1}{n} \right)^n < \sum_{i=0}^n \frac{1}{i!}$

score 70 · Answer 1 · 2026-03-25 07:53:26

70

Views

Prove that $\forall n \in \Bbb{N}, 1 <n, \left( 1 + \frac{1}{n} \right)^n < \sum_{i=0}^n \frac{1}{i!}$

Published on 25 Mar 2026 - 7:53

score 53 · Answer 2 · 2018-02-26 20:10:12

53

Views

Analytical proof of this inequality.

Published on 26 Feb 2018 - 20:10

score 88 · Answer 3 · 2018-02-27 00:37:26

88

Views

Solve the inequality $-1<\frac{x}{\log(x-1)(x-1)}<1$

Published on 27 Feb 2018 - 0:37

score 137 · Answer 4 · 2026-03-21 18:13:17

137

Views

Find minimum value of $\sum \frac {\sqrt a}{\sqrt b +\sqrt c-\sqrt a}$

Published on 21 Mar 2026 - 18:13

score 196 · Answer 5 · 2026-03-25 04:42:54

196

Views

How to prove $e^x\ge \left(1+\frac xn\right)^n$ for any real numbers $x, n > 0$

Published on 25 Mar 2026 - 4:42

score 365 · Answer 6 · 2026-03-28 06:59:58

365

Views

$36 \leq 4(a^3+b^3+c^3+d^3) - (a^4+b^4+c^4+d^4)\leq4 8.$

Published on 28 Mar 2026 - 6:59

score 230 · Answer 7 · 2018-02-27 11:39:53

Proving $\frac{a}{a^2-a+1}+\frac{b}{b^2-b+1}+\frac{c}{c^2-c+1}+\frac{d}{d^2-d+1}\le \frac{8}{3}$ given $a+b+c+d=2$

score 76 · Answer 8 · 2018-02-27 15:05:36

76

Views

Parametric inequality

Published on 27 Feb 2018 - 15:05

score 79 · Answer 9 · 2018-02-27 15:46:55

79

Views

Mean Value Theorem and inequality proving stacking

Published on 27 Feb 2018 - 15:46

score 427 · Answer 10 · 2026-03-29 12:46:17

427

Views

Prove $\sum\limits_{cyc}\sqrt[3]{\frac{a^2+bc}{b+c}}\ge\sqrt[3]{9(a+b+c)}$

Published on 29 Mar 2026 - 12:46

score 15 · Answer 11 · 2026-03-06 23:21:36

15

Views

the question about inequality of $L^p$norm and cut-off function

Published on 06 Mar 2026 - 23:21

score 50 · Answer 12 · 2018-02-27 18:54:29

50

Views

Inequality in $\mathbb{C}$ using continuous functions

Published on 27 Feb 2018 - 18:54

score 49 · Answer 13 · 2018-02-27 19:52:47

49

Views

Square in an Inequality

Published on 27 Feb 2018 - 19:52

score 39 · Answer 14 · 2026-03-25 11:16:53

39

Views

Comparing $\left[(\frac{u+1}{2n})^{2n} - (\frac{u}{2n})^{2n}\right]$ to $\left[(u+1)^n-u^n\right]$

Published on 25 Mar 2026 - 11:16

score 41 · Answer 15 · 2026-03-28 08:49:10

41

Views

Reducing an inequality involving square roots

Published on 28 Mar 2026 - 8:49

List Question

Prove that $\forall n \in \Bbb{N}, 1 <n, \left( 1 + \frac{1}{n} \right)^n < \sum_{i=0}^n \frac{1}{i!}$

Analytical proof of this inequality.

Solve the inequality $-1<\frac{x}{\log(x-1)(x-1)}<1$

Find minimum value of $\sum \frac {\sqrt a}{\sqrt b +\sqrt c-\sqrt a}$

How to prove $e^x\ge \left(1+\frac xn\right)^n$ for any real numbers $x, n > 0$

$36 \leq 4(a^3+b^3+c^3+d^3) - (a^4+b^4+c^4+d^4)\leq4 8.$

Proving $\frac{a}{a^2-a+1}+\frac{b}{b^2-b+1}+\frac{c}{c^2-c+1}+\frac{d}{d^2-d+1}\le \frac{8}{3}$ given $a+b+c+d=2$

Parametric inequality

Mean Value Theorem and inequality proving stacking

Prove $\sum\limits_{cyc}\sqrt[3]{\frac{a^2+bc}{b+c}}\ge\sqrt[3]{9(a+b+c)}$

the question about inequality of $L^p$norm and cut-off function

Inequality in $\mathbb{C}$ using continuous functions

Square in an Inequality

Comparing $\left[(\frac{u+1}{2n})^{2n} - (\frac{u}{2n})^{2n}\right]$ to $\left[(u+1)^n-u^n\right]$

Reducing an inequality involving square roots

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