Question

Prove that $\frac{a}{\sqrt{a^2+1}}+\frac{b}{\sqrt{b^2+1}}+\frac{c}{\sqrt{c^2+1}} \leq \frac{3}{2}$

score 249 · Answer 1 · 2026-03-30 03:42:02

249

Views

Prove that $\frac{a}{\sqrt{a^2+1}}+\frac{b}{\sqrt{b^2+1}}+\frac{c}{\sqrt{c^2+1}} \leq \frac{3}{2}$

Published on 30 Mar 2026 - 3:42

score 703 · Answer 2 · 2026-03-29 18:17:36

703

Views

Square and cubic roots in $\mathbb Q(\sqrt n)$

Published on 29 Mar 2026 - 18:17

score 241 · Answer 3 · 2026-03-29 18:18:38

241

Views

Find the value of the infinite product $\sqrt\frac12\cdot\sqrt{\frac12+\sqrt\frac12}\cdot\sqrt{\frac12+\sqrt{\frac12+\sqrt\frac12}}\cdots$

Published on 29 Mar 2026 - 18:18

score 163 · Answer 4 · 2016-01-10 16:55:34

163

Views

Limit of: $\lim_{n \to \infty}(\sqrt[3]{n^3+\sqrt{n}}-\sqrt[3]{n^3-1})\cdot \sqrt{(3n^3+1)}$

Published on 10 Jan 2016 - 16:55

score 42 · Answer 5 · 2016-01-10 19:21:58

42

Views

Procedure about simplifying radicals

Published on 10 Jan 2016 - 19:21

score 830 · Answer 6 · 2026-04-04 01:53:08

830

Views

Trick to solve this limit $\lim_{x \to\infty} \sqrt{x^2+3x}-x$

Published on 04 Apr 2026 - 1:53

score 3.2k · Answer 7 · 2016-01-11 07:24:04

3.2k

Views

Why is $\sqrt {12} = 2 \sqrt 3$?

Published on 11 Jan 2016 - 7:24

score 21k · Answer 8 · 2016-01-12 10:50:23

21k

Views

I've shown $\lim_{n\to\infty}\sqrt[n]{n}=e$, but it should be $1$. Where's the mistake?

Published on 12 Jan 2016 - 10:50

score 373 · Answer 9 · 2016-01-12 15:04:54

373

Views

Asymptotic bound with square-roots

Published on 12 Jan 2016 - 15:04

score 4.8k · Answer 10 · 2016-01-12 18:09:32

4.8k

Views

Convergence of $\sin{\pi\sqrt{n}}$

Published on 12 Jan 2016 - 18:09

score 132 · Answer 11 · 2016-01-12 22:37:41

132

Views

Limit $\lim_{x \rightarrow \infty} (\sin {\sqrt{1+x}} - \sin {\sqrt{x}})$

Published on 12 Jan 2016 - 22:37

score 83 · Answer 12 · 2026-03-30 14:58:55

83

Views

Find the minimum of $\sum\limits_{cyc} {\sqrt{\frac a{2(b+c)}}}$ with $a,b,c \gt 0$

Published on 30 Mar 2026 - 14:58

score 2.3k · Answer 13 · 2026-03-31 09:42:51

2.3k

Views

Prove that $ax+by+cz+2\sqrt{(xy+yz+xz)(ab+bc+ca)}\le{a+b+c}$

Published on 31 Mar 2026 - 9:42

score 10.9k · Answer 14 · 2016-01-15 18:45:18

10.9k

Views

Simplifying nested square roots ($\sqrt{6-4\sqrt{2}} + \sqrt{2}$)

Published on 15 Jan 2016 - 18:45

score 557 · Answer 15 · 2016-01-16 01:22:19

557

Views

Having issue with tan(7pi/6) converting degrees then to radical

Published on 16 Jan 2016 - 1:22

List Question

Prove that $\frac{a}{\sqrt{a^2+1}}+\frac{b}{\sqrt{b^2+1}}+\frac{c}{\sqrt{c^2+1}} \leq \frac{3}{2}$

Square and cubic roots in $\mathbb Q(\sqrt n)$

Find the value of the infinite product $\sqrt\frac12\cdot\sqrt{\frac12+\sqrt\frac12}\cdot\sqrt{\frac12+\sqrt{\frac12+\sqrt\frac12}}\cdots$

Limit of: $\lim_{n \to \infty}(\sqrt[3]{n^3+\sqrt{n}}-\sqrt[3]{n^3-1})\cdot \sqrt{(3n^3+1)}$

Procedure about simplifying radicals

Trick to solve this limit $\lim_{x \to\infty} \sqrt{x^2+3x}-x$

Why is $\sqrt {12} = 2 \sqrt 3$?

I've shown $\lim_{n\to\infty}\sqrt[n]{n}=e$, but it should be $1$. Where's the mistake?

Asymptotic bound with square-roots

Convergence of $\sin{\pi\sqrt{n}}$

Limit $\lim_{x \rightarrow \infty} (\sin {\sqrt{1+x}} - \sin {\sqrt{x}})$

Find the minimum of $\sum\limits_{cyc} {\sqrt{\frac a{2(b+c)}}}$ with $a,b,c \gt 0$

Prove that $ax+by+cz+2\sqrt{(xy+yz+xz)(ab+bc+ca)}\le{a+b+c}$

Simplifying nested square roots ($\sqrt{6-4\sqrt{2}} + \sqrt{2}$)

Having issue with tan(7pi/6) converting degrees then to radical

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