List questions from cauchy-schwarz-inequality

Published on 25 Mar 2026 - 6:29

119

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Prove this stronger inequality

Published on 23 Mar 2026 - 10:50

306

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Any connections between Cauchy–Schwarz inequality and continuity/boundedness?

Published on 24 Mar 2026 - 22:01

220

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Prove inner-product inequality $\Bigl (\sum_{i=1}^k \langle u\;,\;e_i \rangle \langle v\;,\;e_i \rangle \Bigr)^2≤ \Vert u \Vert^2 \, \Vert v \Vert^2$

Published on 10 May 2018 - 18:22

52

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How to prove $\sum_{i=1}^m \sqrt{t_{i+1}-t_{i}}E(\mathscr{N}_{i})\geq E(\mathscr{N}_{1})\sqrt{t-s}\sqrt{m}$

Published on 25 Mar 2026 - 12:50

399

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Inequality $\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}>1$

Published on 25 Mar 2026 - 9:28

117

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Showing that two vectors are not orthogonal, using Cauchy-Schwarz

Published on 25 Mar 2026 - 19:03

376

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Show using Cauchy-Schwarz inequality

Published on 17 May 2018 - 2:05

162

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Suppose $a,b,c\geq 0$ and $ab+bc+ca=1$, prove that $a\sqrt{a^2+1}+b\sqrt{b^2+1}+c\sqrt{c^2+1}\geq 2$.

Published on 25 Mar 2026 - 17:21

146

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Compute the maximum value of $a + 2b + 3c$

Published on 19 May 2018 - 1:15

342

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Maximizing $3\sin^2 x + 8\sin x\cos x + 9\cos^2 x$. What went wrong?

Published on 19 May 2018 - 2:11

81

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"Cauchy-Schwartz" for symplectic forms

Published on 24 Mar 2026 - 15:15

58

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A geometric inequality in a triangle

Published on 25 Mar 2026 - 15:58

89

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Minimum value of $\frac{x^2+y^2}{x+y}+\frac{y^2+z^2}{y+z}+\frac{z^2+x^2}{z+x}$

Published on 26 Mar 2026 - 12:50

483

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Prove that $3\left(\frac{x}{y} + \frac{y}{z} + \frac{z}{x}\right) \geq 2(x + y + z)\left (\frac{1}{y + z} + \frac{1}{x + z} + \frac{1}{x + y}\right)$

Published on 25 Mar 2026 - 13:38

List Question

Proving that the variance of expectation is greater than the variance of sample mean.

Prove this stronger inequality

Any connections between Cauchy–Schwarz inequality and continuity/boundedness?

Prove inner-product inequality $\Bigl (\sum_{i=1}^k \langle u\;,\;e_i \rangle \langle v\;,\;e_i \rangle \Bigr)^2≤ \Vert u \Vert^2 \, \Vert v \Vert^2$

How to prove $\sum_{i=1}^m \sqrt{t_{i+1}-t_{i}}E(\mathscr{N}_{i})\geq E(\mathscr{N}_{1})\sqrt{t-s}\sqrt{m}$

Inequality $\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}>1$

Showing that two vectors are not orthogonal, using Cauchy-Schwarz

Show using Cauchy-Schwarz inequality

Suppose $a,b,c\geq 0$ and $ab+bc+ca=1$, prove that $a\sqrt{a^2+1}+b\sqrt{b^2+1}+c\sqrt{c^2+1}\geq 2$.

Compute the maximum value of $a + 2b + 3c$

Maximizing $3\sin^2 x + 8\sin x\cos x + 9\cos^2 x$. What went wrong?

"Cauchy-Schwartz" for symplectic forms

A geometric inequality in a triangle

Minimum value of $\frac{x^2+y^2}{x+y}+\frac{y^2+z^2}{y+z}+\frac{z^2+x^2}{z+x}$

Prove that $3\left(\frac{x}{y} + \frac{y}{z} + \frac{z}{x}\right) \geq 2(x + y + z)\left (\frac{1}{y + z} + \frac{1}{x + z} + \frac{1}{x + y}\right)$

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