Question

Proof by induction that $2^n+1 \leq 3^n$ for all positive integers $n$

score 11.6k · Answer 1 · 2026-03-26 19:02:08

11.6k

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Proof by induction that $2^n+1 \leq 3^n$ for all positive integers $n$

Published on 26 Mar 2026 - 19:02

score 226 · Answer 2 · 2018-04-21 06:41:11

226

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Prove inequality $n^{n^2-1} \leq e^{n^n-n}$ for $n = 4, 6, 8, 10, \dots$

Published on 21 Apr 2018 - 6:41

score 664 · Answer 3 · 2026-03-25 07:15:11

664

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An inequality involving three consecutive primes

Published on 25 Mar 2026 - 7:15

score 41 · Answer 4 · 2026-03-26 01:26:35

41

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Trigonometry inequality problem

Published on 26 Mar 2026 - 1:26

score 51 · Answer 5 · 2018-04-21 13:52:18

51

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How to prove that a parametrized linear differential equation solution induces a lipschitz function with respect to the parameter?

Published on 21 Apr 2018 - 13:52

score 49 · Answer 6 · 2018-04-21 16:52:47

49

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An inequality like Bernoulli inequality

Published on 21 Apr 2018 - 16:52

score 64 · Answer 7 · 2026-03-25 06:06:53

64

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let $a,b,c$ be real numbers (not necessarily positive) for which $\min(a+b,b+c,c+a)\ge 2$. Show that $(a+b+c)^3 \ge a^3 + b^3 + c^3 + 24$

Published on 25 Mar 2026 - 6:06

score 64 · Answer 8 · 2026-03-25 21:01:32

64

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Maximum value of $2(\sin A + \sin B) - 2\cos C$

Published on 25 Mar 2026 - 21:01

score 495 · Answer 9 · 2026-03-25 10:55:34

495

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Is $|\langle Ax,x\rangle| \leq \langle |A|x,x\rangle$ in a complex Hilbert space?

Published on 25 Mar 2026 - 10:55

score 78 · Answer 10 · 2018-04-23 01:26:42

78

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What inequalities involve sums of products of the form $\sum_{(i_1, \ldots , i_N) \in S_N ^{(n)}} \prod_{j=1} ^ N i_j \quad?$

Published on 23 Apr 2018 - 1:26

score 60 · Answer 11 · 2026-03-25 16:01:11

60

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Can we add absolute value to inequality that already have absolute value?

Published on 25 Mar 2026 - 16:01

score 450 · Answer 12 · 2026-03-28 08:09:57

450

Views

Convexity of $\frac x{\sin x},\,\forall x\in[0,\pi)$

Published on 28 Mar 2026 - 8:09

score 74 · Answer 13 · 2026-03-25 04:41:03

74

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Does the inequality $|\frac{1-x}{(\sqrt x +1)^2}|<1$ hold for $x>0$?

Published on 25 Mar 2026 - 4:41

score 79 · Answer 14 · 2018-04-23 08:56:14

79

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What is the area of the region $R$ if $R=\{(x,y):x^2+y^2\le100$, $\sin(x+y)>0\}$?

Published on 23 Apr 2018 - 8:56

score 273 · Answer 15 · 2018-04-23 11:01:50

273

Views

When will discrete Hardy's inequality become equality?

Published on 23 Apr 2018 - 11:01

List Question

Proof by induction that $2^n+1 \leq 3^n$ for all positive integers $n$

Prove inequality $n^{n^2-1} \leq e^{n^n-n}$ for $n = 4, 6, 8, 10, \dots$

An inequality involving three consecutive primes

Trigonometry inequality problem

How to prove that a parametrized linear differential equation solution induces a lipschitz function with respect to the parameter?

An inequality like Bernoulli inequality

let $a,b,c$ be real numbers (not necessarily positive) for which $\min(a+b,b+c,c+a)\ge 2$. Show that $(a+b+c)^3 \ge a^3 + b^3 + c^3 + 24$

Maximum value of $2(\sin A + \sin B) - 2\cos C$

Is $|\langle Ax,x\rangle| \leq \langle |A|x,x\rangle$ in a complex Hilbert space?

What inequalities involve sums of products of the form $\sum_{(i_1, \ldots , i_N) \in S_N ^{(n)}} \prod_{j=1} ^ N i_j \quad?$

Can we add absolute value to inequality that already have absolute value?

Convexity of $\frac x{\sin x},\,\forall x\in[0,\pi)$

Does the inequality $|\frac{1-x}{(\sqrt x +1)^2}|<1$ hold for $x>0$?

What is the area of the region $R$ if $R=\{(x,y):x^2+y^2\le100$, $\sin(x+y)>0\}$?

When will discrete Hardy's inequality become equality?

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