Question

If $a_i>0$ and $\sum_{i=1}^n a_i = 1$, then $\sum_{i=1}^n \frac{1}{a_i} \geq n^2$?

score 109 · Answer 1 · 2026-03-22 19:31:59

109

Views

If $a_i>0$ and $\sum_{i=1}^n a_i = 1$, then $\sum_{i=1}^n \frac{1}{a_i} \geq n^2$?

Published on 22 Mar 2026 - 19:31

score 73 · Answer 2 · 2026-04-02 08:45:08

73

Views

Is $\int_{A_t} \frac{1}{|x_j|^{p}}\, dx \leq \sum_{j=1}^{d} \int_{A_{j,t}}\frac{1}{|x_j|^p}\, dx \leq \int_{A_t} \frac{1}{|x|^p} \,dx$?

Published on 02 Apr 2026 - 8:45

score 258 · Answer 3 · 2026-03-24 23:43:20

258

Views

quadratic form inequality for SPD matrices

Published on 24 Mar 2026 - 23:43

score 497 · Answer 4 · 2026-03-27 12:29:43

497

Views

Trace of positive semidefinite matrix

Published on 27 Mar 2026 - 12:29

score 53 · Answer 5 · 2026-03-26 02:55:47

53

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Is Var[max{ a, min{X, b}}] <= Var[X] for a < b and X being normally distributed?

Published on 26 Mar 2026 - 2:55

score 159 · Answer 6 · 2026-03-24 22:01:44

159

Views

$\sum_{k=1}^{n} \frac{1}{n+k} < \ln 2$

Published on 24 Mar 2026 - 22:01

score 107 · Answer 7 · 2026-03-25 03:00:46

107

Views

Problem of Inequality using wavy curve

Published on 25 Mar 2026 - 3:00

score 162 · Answer 8 · 2026-03-25 17:21:47

162

Views

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

score 127 · Answer 9 · 2018-05-18 06:15:37

To show that $\max\limits_{1\leq i\leq n}|x_i-\bar{x}|<\frac{n-1}{\sqrt n}\sqrt{\frac1{n-1}\smash[b]{\sum\limits_{i=1}^n}(x_i-\bar{x})^2}$

score 27 · Answer 10 · 2018-05-18 07:07:54

Another inequality : $|\sum_{i=1}^n b_ix_i|\leq\frac{x_{(n)}-x_{(1)}}{2}$ where $\sum_{i=1}^n b_i = 0$ and $\sum_{i=1}^n |b_i| = 1$

score 65 · Answer 11 · 2026-03-25 12:51:00

65

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An inequality regarding mean and standard deviation : $\frac{1}{n}\#x_i \in (\bar{x}-ks,\bar{x}+ks) \geq 1-\frac{1}{k^2}$

Published on 25 Mar 2026 - 12:51

score 48 · Answer 12 · 2018-05-18 14:32:44

48

Views

Which solution to the given inequality is correct?

Published on 18 May 2018 - 14:32

score 562 · Answer 13 · 2018-05-18 16:41:50

562

Views

How to show that $uv \le \frac {u^p}{p}+ \frac {v^q}{q}$ where $\frac 1p + \frac 1q = 1$

Published on 18 May 2018 - 16:41

score 489 · Answer 14 · 2026-03-26 06:32:36

489

Views

If $x \in R $ and $\frac{(x-a)(x-c)}{(x-b)}$ can assume any real value, then which of the following may be correct

Published on 26 Mar 2026 - 6:32

score 57 · Answer 15 · 2018-05-19 00:59:18

57

Views

Error of sample median of uniform variables

Published on 19 May 2018 - 0:59

List Question

If $a_i>0$ and $\sum_{i=1}^n a_i = 1$, then $\sum_{i=1}^n \frac{1}{a_i} \geq n^2$?

Is $\int_{A_t} \frac{1}{|x_j|^{p}}\, dx \leq \sum_{j=1}^{d} \int_{A_{j,t}}\frac{1}{|x_j|^p}\, dx \leq \int_{A_t} \frac{1}{|x|^p} \,dx$?

quadratic form inequality for SPD matrices

Trace of positive semidefinite matrix

Is Var[max{ a, min{X, b}}] <= Var[X] for a < b and X being normally distributed?

$\sum_{k=1}^{n} \frac{1}{n+k} < \ln 2$

Problem of Inequality using wavy curve

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

To show that $\max\limits_{1\leq i\leq n}|x_i-\bar{x}|<\frac{n-1}{\sqrt n}\sqrt{\frac1{n-1}\smash[b]{\sum\limits_{i=1}^n}(x_i-\bar{x})^2}$

Another inequality : $|\sum_{i=1}^n b_ix_i|\leq\frac{x_{(n)}-x_{(1)}}{2}$ where $\sum_{i=1}^n b_i = 0$ and $\sum_{i=1}^n |b_i| = 1$

An inequality regarding mean and standard deviation : $\frac{1}{n}\#x_i \in (\bar{x}-ks,\bar{x}+ks) \geq 1-\frac{1}{k^2}$

Which solution to the given inequality is correct?

How to show that $uv \le \frac {u^p}{p}+ \frac {v^q}{q}$ where $\frac 1p + \frac 1q = 1$

If $x \in R $ and $\frac{(x-a)(x-c)}{(x-b)}$ can assume any real value, then which of the following may be correct

Error of sample median of uniform variables

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