Question

How to prove: $\sum_{i=1}^{k}|x_{i+1}-x_{i}| \geq \max_{i \in [k+1]}x_{i} - \min_{i \in [k+1]}x_{i}$?

score 43 · Answer 1 · 2018-08-07 15:10:08

43

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How to prove: $\sum_{i=1}^{k}|x_{i+1}-x_{i}| \geq \max_{i \in [k+1]}x_{i} - \min_{i \in [k+1]}x_{i}$?

Published on 07 Aug 2018 - 15:10

score 201 · Answer 2 · 2026-03-25 19:06:30

201

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Prove that: $\frac{bc}{a^2+1}+\frac{ac}{b^2+1}+\frac{ab}{c^2+1}\leq \frac{3}{4}$

Published on 25 Mar 2026 - 19:06

score 70 · Answer 3 · 2026-03-26 14:20:24

70

Views

Inequality with floor and a fraction

Published on 26 Mar 2026 - 14:20

score 199 · Answer 4 · 2026-03-26 08:00:32

199

Views

How to prove $1 + \frac{1}{\sqrt{2}} +... +\frac{1}{\sqrt{n}} <\sqrt{n}\ .\left(2n-1\right)^{1/4} $

Published on 26 Mar 2026 - 8:00

score 1.5k · Answer 5 · 2026-03-26 01:17:29

1.5k

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Largest possible value of trigonometric functions

Published on 26 Mar 2026 - 1:17

score 154 · Answer 6 · 2018-08-08 12:41:00

154

Views

$\max_i x_i\ \leq \log \sum_{i} e^{x_i}$?

Published on 08 Aug 2018 - 12:41

score 219 · Answer 7 · 2026-03-25 01:20:32

219

Views

Prove that inequality $1+\frac{1}{2\sqrt{2}}+...+\frac{1}{n\sqrt{n}}<2\sqrt{2}$

Published on 25 Mar 2026 - 1:20

score 72 · Answer 8 · 2018-08-08 16:04:16

72

Views

Inequalities and Square Root

Published on 08 Aug 2018 - 16:04

score 558 · Answer 9 · 2026-03-26 01:16:42

558

Views

Prove that $\log_n(n+1)\geq\log_{n+1}(n+2)$ for $n>1$

Published on 26 Mar 2026 - 1:16

score 156 · Answer 10 · 2018-08-08 19:55:26

156

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$\int_0^1 xf(x)\,dx \le \int_0^1 \frac{2}{3}f(x)\,dx$ for a concave function $f(x)$

Published on 08 Aug 2018 - 19:55

score 62 · Answer 11 · 2026-03-25 12:28:08

62

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$|\int_{0}^{x} f(s) ds|^2\leq 2\sqrt{x}\int_{0}^{x} \sqrt{s} |f(s)|^2 ds$

Published on 25 Mar 2026 - 12:28

score 191 · Answer 12 · 2026-03-22 13:03:48

191

Views

Inequality $(1+x^k)^{k+1}\geq (1+x^{k+1})^k$

Published on 22 Mar 2026 - 13:03

score 303 · Answer 13 · 2026-03-25 12:13:44

303

Views

Convolution by $\log$ maps $\mathrm{L}^1$ into $\mathrm{BMO}$

Published on 25 Mar 2026 - 12:13

score 117 · Answer 14 · 2026-03-25 10:55:47

117

Views

What bound does Chebychev’s inequality give for $P(Y ≥ 3 \text{ or } Y ≤ 1)$?

Published on 25 Mar 2026 - 10:55

score 138 · Answer 15 · 2018-08-09 09:01:59

138

Views

Ordered pairs that satisfy inequalities

Published on 09 Aug 2018 - 9:01

List Question

How to prove: $\sum_{i=1}^{k}|x_{i+1}-x_{i}| \geq \max_{i \in [k+1]}x_{i} - \min_{i \in [k+1]}x_{i}$?

Prove that: $\frac{bc}{a^2+1}+\frac{ac}{b^2+1}+\frac{ab}{c^2+1}\leq \frac{3}{4}$

Inequality with floor and a fraction

How to prove $1 + \frac{1}{\sqrt{2}} +... +\frac{1}{\sqrt{n}} <\sqrt{n}\ .\left(2n-1\right)^{1/4} $

Largest possible value of trigonometric functions

$\max_i x_i\ \leq \log \sum_{i} e^{x_i}$?

Prove that inequality $1+\frac{1}{2\sqrt{2}}+...+\frac{1}{n\sqrt{n}}<2\sqrt{2}$

Inequalities and Square Root

Prove that $\log_n(n+1)\geq\log_{n+1}(n+2)$ for $n>1$

$\int_0^1 xf(x)\,dx \le \int_0^1 \frac{2}{3}f(x)\,dx$ for a concave function $f(x)$

$|\int_{0}^{x} f(s) ds|^2\leq 2\sqrt{x}\int_{0}^{x} \sqrt{s} |f(s)|^2 ds$

Inequality $(1+x^k)^{k+1}\geq (1+x^{k+1})^k$

Convolution by $\log$ maps $\mathrm{L}^1$ into $\mathrm{BMO}$

What bound does Chebychev’s inequality give for $P(Y ≥ 3 \text{ or } Y ≤ 1)$?

Ordered pairs that satisfy inequalities

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