Question

Inequality: $0<\alpha<1$, $(\sum_{i=1}^na_i)^{\alpha} \leq \sum_{i=1}^na_i^\alpha$

score 140 · Answer 1 · 2026-04-01 12:51:17

140

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Inequality: $0<\alpha<1$, $(\sum_{i=1}^na_i)^{\alpha} \leq \sum_{i=1}^na_i^\alpha$

Published on 01 Apr 2026 - 12:51

score 41 · Answer 2 · 2026-04-13 17:25:31

41

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score 4.2k · Answer 3 · 2026-04-14 09:48:31

4.2k

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score 142 · Answer 4 · 2026-04-20 11:10:21

142

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score 124 · Answer 5 · 2026-04-17 09:03:25

124

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score 47 · Answer 6 · 2026-04-16 06:28:49

47

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score 69 · Answer 7 · 2026-04-25 16:39:28

69

Views

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score 73 · Answer 8 · 2026-04-17 07:16:14

73

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I need to show that functional series $\sum_{n=1}^{+\infty}\frac{\sqrt{n+x^2}}{n^2+e^x}$ is differentiable

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score 242 · Answer 9 · 2026-04-14 02:56:36

242

Views

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score 41 · Answer 10 · 2026-04-22 06:23:50

41

Views

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Published on 22 Apr 2026 - 6:23

score 22 · Answer 11 · 2026-04-16 16:04:10

22

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calculate derivative $\frac{1}{2}(x+\alpha p)^T A(x+\alpha p)-b^T(x+\alpha p)$ about $\alpha$

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score 527 · Answer 12 · 2026-05-10 14:55:26

527

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score 166 · Answer 13 · 2026-05-10 19:26:24

166

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score 38 · Answer 14 · 2026-04-14 15:55:40

38

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score 255 · Answer 15 · 2026-04-24 03:44:36

255

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List Question

Inequality: $0<\alpha<1$, $(\sum_{i=1}^na_i)^{\alpha} \leq \sum_{i=1}^na_i^\alpha$

Curves and Surfaces

Second order differential equations with substitution help

How to prove this specific function has limit either $\infty$ or 0?

Prove or disprove that $(b-a)^2(\log(b)-\log(a))^{-2}\ge ab$ for all $a,b>0$

Which Geometry Shape Is $3x^2+3y^2-10y+3=0$

$e^{-c\sin \theta}$ integral evaluation

I need to show that functional series $\sum_{n=1}^{+\infty}\frac{\sqrt{n+x^2}}{n^2+e^x}$ is differentiable

How does the fractional part of $a^n$ behave at infinity？

Find the residues of branches of form $e^{\frac1{1+\sqrt(z)}}dz$

calculate derivative $\frac{1}{2}(x+\alpha p)^T A(x+\alpha p)-b^T(x+\alpha p)$ about $\alpha$

Continuous rotation formula of turning particle

"by symmetry" argument when showing that two curves are orthogonal.

Multivariable Inverse

Exact Euler Maclaurin summation formula

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