Question

Show that $c_nX_n \overset{p}{\to}cX$ if $X_n \overset{p}{\to}X$ and $c_n$ is a sequence of reals which converges to the limit $c \in(0,\infty)$.

score 152 · Answer 1 · 2026-04-07 00:42:06

152

Views

Show that $c_nX_n \overset{p}{\to}cX$ if $X_n \overset{p}{\to}X$ and $c_n$ is a sequence of reals which converges to the limit $c \in(0,\infty)$.

Published on 07 Apr 2026 - 0:42

score 194 · Answer 2 · 2026-04-06 00:17:14

194

Views

Solution of a quadratic equation to satisfy a constraint

Published on 06 Apr 2026 - 0:17

score 129 · Answer 3 · 2018-09-23 16:27:32

Inequality Proof: $\frac{a(a^2-b^2)}{13a^2+5b^2} + \frac{b(b^2-c^2)}{13b^2+5c^2} + \frac{c(c^2-a^2)}{13c^2+5a^2} \geq 0$

score 85 · Answer 4 · 2026-03-28 14:19:38

85

Views

Show for all n ∈ IN that the inequality $(n!)^2<2^{n^{2}}$ holds (by induction)

Published on 28 Mar 2026 - 14:19

score 120 · Answer 5 · 2018-09-23 21:12:26

120

Views

Proof inequality $a,b, c \in [0,1]$

Published on 23 Sep 2018 - 21:12

score 67 · Answer 6 · 2018-09-24 01:02:09

67

Views

Show $\left|\frac{e^{iz}}{z^2+1}\right|\leq\frac{1}{R^2-1}$ for $R>1$ and $z\in\text{Range}(\gamma_R)$

Published on 24 Sep 2018 - 1:02

score 45 · Answer 7 · 2018-09-24 09:57:06

45

Views

Sufficient condition for an inequality to hold

Published on 24 Sep 2018 - 9:57

score 71 · Answer 8 · 2018-09-24 15:29:20

71

Views

Complex Square root bound

Published on 24 Sep 2018 - 15:29

score 188 · Answer 9 · 2026-03-28 16:58:00

188

Views

How to show that $x^{\tfrac{1}{p}}\leq \frac{1}{p}x+\frac{1}{q}$

Published on 28 Mar 2026 - 16:58

score 32 · Answer 10 · 2026-03-28 17:00:04

32

Views

Weird inequality with $l^1$-norm

Published on 28 Mar 2026 - 17:00

score 127 · Answer 11 · 2018-09-24 20:20:35

127

Views

how to prove $f'(x) \leq \frac{f(x) - f(y)}{x - y} \leq f'(y) $

Published on 24 Sep 2018 - 20:20

score 852 · Answer 12 · 2018-09-24 22:43:38

852

Views

Solving $\sqrt{8-x^2}-\sqrt{25-x^2}\geq x$

Published on 24 Sep 2018 - 22:43

score 155 · Answer 13 · 2026-03-26 02:50:21

155

Views

Prove $n^3+(n+1)^3>(n+2)^3$

Published on 26 Mar 2026 - 2:50

score 67 · Answer 14 · 2026-03-28 15:55:38

67

Views

Induction for inequality

Published on 28 Mar 2026 - 15:55

score 134 · Answer 15 · 2026-03-25 22:05:09

134

Views

If $\sum\limits_{\text{cyc}}x=\frac\pi2$, then $2\sqrt{\sum\limits_{\text{cyc}}\tan x}\le\sum\limits_{\text{cyc}}\frac{\sqrt{\tan x}}{\cos x}$

Published on 25 Mar 2026 - 22:05

List Question

Show that $c_nX_n \overset{p}{\to}cX$ if $X_n \overset{p}{\to}X$ and $c_n$ is a sequence of reals which converges to the limit $c \in(0,\infty)$.

Solution of a quadratic equation to satisfy a constraint

Inequality Proof: $\frac{a(a^2-b^2)}{13a^2+5b^2} + \frac{b(b^2-c^2)}{13b^2+5c^2} + \frac{c(c^2-a^2)}{13c^2+5a^2} \geq 0$

Show for all n ∈ IN that the inequality $(n!)^2<2^{n^{2}}$ holds (by induction)

Proof inequality $a,b, c \in [0,1]$

Show $\left|\frac{e^{iz}}{z^2+1}\right|\leq\frac{1}{R^2-1}$ for $R>1$ and $z\in\text{Range}(\gamma_R)$

Sufficient condition for an inequality to hold

Complex Square root bound

How to show that $x^{\tfrac{1}{p}}\leq \frac{1}{p}x+\frac{1}{q}$

Weird inequality with $l^1$-norm

how to prove $f'(x) \leq \frac{f(x) - f(y)}{x - y} \leq f'(y) $

Solving $\sqrt{8-x^2}-\sqrt{25-x^2}\geq x$

Prove $n^3+(n+1)^3>(n+2)^3$

Induction for inequality

If $\sum\limits_{\text{cyc}}x=\frac\pi2$, then $2\sqrt{\sum\limits_{\text{cyc}}\tan x}\le\sum\limits_{\text{cyc}}\frac{\sqrt{\tan x}}{\cos x}$

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