Question

Showing that $\sqrt{\sum_{k=1}^{n} |u_k|^2}\leq \sum_{k=1}^{n}|u_k| \leq n\cdot\max\{|u_k|:1\leq k \leq n\}$

score 73 · Answer 1 · 2026-03-27 13:48:17

Showing that $\sqrt{\sum_{k=1}^{n} |u_k|^2}\leq \sum_{k=1}^{n}|u_k| \leq n\cdot\max\{|u_k|:1\leq k \leq n\}$

Published on 27 Mar 2026 - 13:48

score 170 · Answer 2 · 2026-03-28 08:50:02

Prove that if $a_k \in [0, 1] $ then $\frac {1}{1+a_1} + \frac {1}{1+a_2} + \cdots +\frac {1}{1+a_n} \le \frac{n}{1+ \sqrt[n]{a_1a_2\cdots a_n}}$.

score 50 · Answer 3 · 2018-11-29 17:58:24

50

Views

$x,y \in R$ and $x \neq y$ Show that $e^\frac{x+y}2 \lt \frac12 (e^x + e^y)$

Published on 29 Nov 2018 - 17:58

score 149 · Answer 4 · 2018-11-29 19:55:48

149

Views

If $f:[0,1]\to[0,1]$ is such that $f(x) \leq 2 \int_0^x f(t) dt$, show that $f(x)=0$ on its domain

Published on 29 Nov 2018 - 19:55

score 266 · Answer 5 · 2026-03-25 04:55:33

266

Views

Jensen's type inequality for inner product

Published on 25 Mar 2026 - 4:55

score 302 · Answer 6 · 2026-04-12 17:41:07

302

Views

Inequality for convex combination inner product

Published on 12 Apr 2026 - 17:41

score 44 · Answer 7 · 2018-11-29 23:14:39

44

Views

Proof that $\frac{1+x^2}{n^2} \geq 1-e^{-x^2/n^2}$ for all $x,n \in \mathbb{R}$

Published on 29 Nov 2018 - 23:14

score 328 · Answer 8 · 2026-03-28 08:50:10

328

Views

If $a+b+c=\frac 1a +\frac 1b +\frac 1c$ then prove that $ab+bc+ca \geq 3$

Published on 28 Mar 2026 - 8:50

score 97 · Answer 9 · 2026-04-09 03:51:15

97

Views

Little inequality

Published on 09 Apr 2026 - 3:51

score 193 · Answer 10 · 2026-03-28 11:54:07

193

Views

$f$ is T periodic and $f(x) + f'(x) \ge 0 \Rightarrow f(x) \ge 0$

Published on 28 Mar 2026 - 11:54

score 113 · Answer 11 · 2026-04-12 23:38:00

113

Views

Proof using AM-GM inequality

Published on 12 Apr 2026 - 23:38

score 91 · Answer 12 · 2026-04-13 02:21:46

91

Views

Prove or disprove an inequality problem

Published on 13 Apr 2026 - 2:21

score 229 · Answer 13 · 2026-03-25 22:10:51

229

Views

Maximum of $ab+2bc+3ca$ with $a^4+b^4+c^4=1$

Published on 25 Mar 2026 - 22:10

score 258 · Answer 14 · 2018-11-30 18:55:09

258

Views

Suppose $f: [0,1] \rightarrow [0,1] $ and $f(x) \leq \int_0^x \sqrt{f(t)}dt$. Show that $f(x) \leq x^2$ for all $x \in [0,1]$.

Published on 30 Nov 2018 - 18:55

score 49 · Answer 15 · 2018-11-30 19:12:31

49

Views

Is it true for any real $a$ and $b$ that if $a*b > 0$ => $a/b>0$?

Published on 30 Nov 2018 - 19:12

List Question

Showing that $\sqrt{\sum_{k=1}^{n} |u_k|^2}\leq \sum_{k=1}^{n}|u_k| \leq n\cdot\max\{|u_k|:1\leq k \leq n\}$

Prove that if $a_k \in [0, 1] $ then $\frac {1}{1+a_1} + \frac {1}{1+a_2} + \cdots +\frac {1}{1+a_n} \le \frac{n}{1+ \sqrt[n]{a_1a_2\cdots a_n}}$.

$x,y \in R$ and $x \neq y$ Show that $e^\frac{x+y}2 \lt \frac12 (e^x + e^y)$

If $f:[0,1]\to[0,1]$ is such that $f(x) \leq 2 \int_0^x f(t) dt$, show that $f(x)=0$ on its domain

Jensen's type inequality for inner product

Inequality for convex combination inner product

Proof that $\frac{1+x^2}{n^2} \geq 1-e^{-x^2/n^2}$ for all $x,n \in \mathbb{R}$

If $a+b+c=\frac 1a +\frac 1b +\frac 1c$ then prove that $ab+bc+ca \geq 3$

Little inequality

$f$ is T periodic and $f(x) + f'(x) \ge 0 \Rightarrow f(x) \ge 0$

Proof using AM-GM inequality

Prove or disprove an inequality problem

Maximum of $ab+2bc+3ca$ with $a^4+b^4+c^4=1$

Suppose $f: [0,1] \rightarrow [0,1] $ and $f(x) \leq \int_0^x \sqrt{f(t)}dt$. Show that $f(x) \leq x^2$ for all $x \in [0,1]$.

Is it true for any real $a$ and $b$ that if $a*b > 0$ => $a/b>0$?

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