Question

prove $ H(x)\geq \ln(x)(\ln (1 - x))$ for $ 0\lt x\lt 1$

score 220 · Answer 1 · 2026-04-16 15:57:47

220

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prove $ H(x)\geq \ln(x)(\ln (1 - x))$ for $ 0\lt x\lt 1$

Published on 16 Apr 2026 - 15:57

score 44 · Answer 2 · 2026-04-12 19:05:18

44

Views

How to show this inequality involving generalized Fibonacci sequence?

Published on 12 Apr 2026 - 19:05

score 110 · Answer 3 · 2026-04-17 14:39:46

110

Views

Proving $\int_a^b\sqrt{f^2+g^2}\ge\sqrt{(\int_a^b f)^2 + (\int_a^b g)^2 } $ without using $|\int_a^b z(t)\,dt|\le\int_a^b |z(t)|\,dt$

Published on 17 Apr 2026 - 14:39

score 312 · Answer 4 · 2026-04-15 05:38:45

312

Views

Proving multiplication floor functions

Published on 15 Apr 2026 - 5:38

score 61 · Answer 5 · 2026-04-11 13:21:02

61

Views

Absolute Value Inequality (another)

Published on 11 Apr 2026 - 13:21

score 52 · Answer 6 · 2026-04-14 00:15:11

If $\frac{a}{b}<\frac{a'}{b'}<\frac{a''}{b''}$, with all values positive, then $\frac{a}{b}<\frac{ab+a’b’+a’’b’’}{b^2+b’^2+b’’^2}<\frac{a’’}{b’’}$

score 656 · Answer 7 · 2026-04-17 12:06:28

656

Views

Check my proof of 0 < |r - q| < epsilon. (Real # - Rational #)

Published on 17 Apr 2026 - 12:06

score 305 · Answer 8 · 2026-04-16 23:00:46

305

Views

Generalization of $(a+b)^2\leq 2(a^2+b^2)$

Published on 16 Apr 2026 - 23:00

score 160 · Answer 9 · 2026-04-16 13:55:37

160

Views

Solve the inequality $\frac{2}{x} > 3 x$

Published on 16 Apr 2026 - 13:55

score 143 · Answer 10 · 2026-04-14 18:05:10

143

Views

Prove $\frac{\ln{n}}{\sqrt{n+1}} > \frac{\ln{(n+1)}}{\sqrt{n+2}}$

Published on 14 Apr 2026 - 18:05

score 104 · Answer 11 · 2026-04-15 05:52:15

104

Views

How to find the range of $y=\frac{x^2+1}{x+1}$ without using derivative?

Published on 15 Apr 2026 - 5:52

score 468 · Answer 12 · 2026-04-14 21:15:10

Reverse Littlewood-Offord problem: lower bound for the number of choices of signs such that $|\pm a_1\dots\pm a_n| \leq \max|a_i|.$

score 144 · Answer 13 · 2026-03-25 16:02:07

144

Views

Prove $\Sigma_{cyc}(\frac{a}{b-c}-3)^4\ge193$

Published on 25 Mar 2026 - 16:02

score 117 · Answer 14 · 2026-04-14 01:27:35

117

Views

Upper bound like $O(\log T)$ for the following sum of square root.

Published on 14 Apr 2026 - 1:27

score 91 · Answer 15 · 2026-04-16 06:50:56

91

Views

How to show $(u^{3/2}+v^{3/2})^{2/3} \leq u+v$ where $u,v \geq 0$?

Published on 16 Apr 2026 - 6:50

List Question

prove $ H(x)\geq \ln(x)(\ln (1 - x))$ for $ 0\lt x\lt 1$

How to show this inequality involving generalized Fibonacci sequence?

Proving $\int_a^b\sqrt{f^2+g^2}\ge\sqrt{(\int_a^b f)^2 + (\int_a^b g)^2 } $ without using $|\int_a^b z(t)\,dt|\le\int_a^b |z(t)|\,dt$

Proving multiplication floor functions

Absolute Value Inequality (another)

If $\frac{a}{b}<\frac{a'}{b'}<\frac{a''}{b''}$, with all values positive, then $\frac{a}{b}<\frac{ab+a’b’+a’’b’’}{b^2+b’^2+b’’^2}<\frac{a’’}{b’’}$

Check my proof of 0 < |r - q| < epsilon. (Real # - Rational #)

Generalization of $(a+b)^2\leq 2(a^2+b^2)$

Solve the inequality $\frac{2}{x} > 3 x$

Prove $\frac{\ln{n}}{\sqrt{n+1}} > \frac{\ln{(n+1)}}{\sqrt{n+2}}$

How to find the range of $y=\frac{x^2+1}{x+1}$ without using derivative?

Reverse Littlewood-Offord problem: lower bound for the number of choices of signs such that $|\pm a_1\dots\pm a_n| \leq \max|a_i|.$

Prove $\Sigma_{cyc}(\frac{a}{b-c}-3)^4\ge193$

Upper bound like $O(\log T)$ for the following sum of square root.

How to show $(u^{3/2}+v^{3/2})^{2/3} \leq u+v$ where $u,v \geq 0$?

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