Question

Proving $\prod_{t=1}^{T}\sqrt{1-4x_t^{2}}\leq \exp\left(-2\sum_{t=1}^{T}x_t^{2}\right)$, given $1-x\leq \exp(-x)$

score 61 · Answer 1 · 2026-03-28 16:14:13

61

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Proving $\prod_{t=1}^{T}\sqrt{1-4x_t^{2}}\leq \exp\left(-2\sum_{t=1}^{T}x_t^{2}\right)$, given $1-x\leq \exp(-x)$

Published on 28 Mar 2026 - 16:14

score 47 · Answer 2 · 2026-04-10 14:53:27

47

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complex numbers inequality proof

Published on 10 Apr 2026 - 14:53

score 153 · Answer 3 · 2026-03-25 17:42:00

153

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Proof verification of if $\{x_n\}$ is monotone then $\{y_n\} = {1\over x_1 + x_2 + \dots + x_n}$ is monotone

Published on 25 Mar 2026 - 17:42

score 368 · Answer 4 · 2026-04-02 19:15:31

368

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How to prove the logaritmic inequality: $\ 1- \frac{a}{b} < \ln(b)-\ln(a)<\frac{b}{a} - 1$?

Published on 02 Apr 2026 - 19:15

score 51 · Answer 5 · 2026-03-25 17:40:44

51

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Proof verification of $\{x_n\} = \left(1 + {1\over 2n}\right)^n$ is an increasing sequence.

Published on 25 Mar 2026 - 17:40

score 149 · Answer 6 · 2026-03-29 18:34:26

149

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Find all the continuous functions that satisfy $[f(t)]^2=F(t)-F(0)$

Published on 29 Mar 2026 - 18:34

score 426 · Answer 7 · 2026-03-24 22:01:45

426

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How can you prove that $1.05^{50} < 100$ without a calculator?

Published on 24 Mar 2026 - 22:01

score 153 · Answer 8 · 2026-03-28 02:06:41

The greatest $M$ that $\sqrt[5]{\frac{a}{b+c}}+\sqrt[5]{\frac{b}{c+d}}+\sqrt[5]{\frac{c}{d+e}}+\sqrt[5]{\frac{d}{e+a}}+\sqrt[5]{\frac{e}{a+b}}>M$

score 123 · Answer 9 · 2018-11-08 21:10:21

123

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Find all the values for $x$: $\sin(x) < 0,6$

Published on 08 Nov 2018 - 21:10

score 61 · Answer 10 · 2026-03-29 16:50:12

61

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Prove that $f(t)$ satisfies the following inequality

Published on 29 Mar 2026 - 16:50

score 286 · Answer 11 · 2026-04-12 00:41:39

286

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Prove a matrix norm inequality

Published on 12 Apr 2026 - 0:41

score 82 · Answer 12 · 2026-04-09 15:54:42

82

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Induction on a series with absolute value

Published on 09 Apr 2026 - 15:54

score 135 · Answer 13 · 2026-03-25 14:18:35

135

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Problem wih hyperbolic function

Published on 25 Mar 2026 - 14:18

score 103 · Answer 14 · 2026-04-11 16:35:31

103

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Solving inequality involving exponents

Published on 11 Apr 2026 - 16:35

score 637 · Answer 15 · 2026-03-25 03:22:15

637

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$\frac{a}{\sqrt{a^2 + 8bc}} +\frac{b}{\sqrt{b^2 + 8ac}} + \frac{c}{\sqrt{c^2 + 8ab}} \ge \frac{1}{\sqrt{a^3+b^3+c^3 + 24abc}}$ is true?

Published on 25 Mar 2026 - 3:22

List Question

Proving $\prod_{t=1}^{T}\sqrt{1-4x_t^{2}}\leq \exp\left(-2\sum_{t=1}^{T}x_t^{2}\right)$, given $1-x\leq \exp(-x)$

complex numbers inequality proof

Proof verification of if $\{x_n\}$ is monotone then $\{y_n\} = {1\over x_1 + x_2 + \dots + x_n}$ is monotone

How to prove the logaritmic inequality: $\ 1- \frac{a}{b} < \ln(b)-\ln(a)<\frac{b}{a} - 1$?

Proof verification of $\{x_n\} = \left(1 + {1\over 2n}\right)^n$ is an increasing sequence.

Find all the continuous functions that satisfy $[f(t)]^2=F(t)-F(0)$

How can you prove that $1.05^{50} < 100$ without a calculator?

The greatest $M$ that $\sqrt[5]{\frac{a}{b+c}}+\sqrt[5]{\frac{b}{c+d}}+\sqrt[5]{\frac{c}{d+e}}+\sqrt[5]{\frac{d}{e+a}}+\sqrt[5]{\frac{e}{a+b}}>M$

Find all the values for $x$: $\sin(x) < 0,6$

Prove that $f(t)$ satisfies the following inequality

Prove a matrix norm inequality

Induction on a series with absolute value

Problem wih hyperbolic function

Solving inequality involving exponents

$\frac{a}{\sqrt{a^2 + 8bc}} +\frac{b}{\sqrt{b^2 + 8ac}} + \frac{c}{\sqrt{c^2 + 8ab}} \ge \frac{1}{\sqrt{a^3+b^3+c^3 + 24abc}}$ is true?

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