Question

If $n\in \mathbb{N},$ then $(1-1/2) (1-1/4)(1-1/8)(1-1/16)...(1-1/2^n)\geq 1/4+1/2^{n+1}.$

score 774 · Answer 1 · 2026-03-26 11:01:24

774

Views

If $n\in \mathbb{N},$ then $(1-1/2) (1-1/4)(1-1/8)(1-1/16)...(1-1/2^n)\geq 1/4+1/2^{n+1}.$

Published on 26 Mar 2026 - 11:01

score 185 · Answer 2 · 2018-03-30 11:15:43

185

Views

Inequality with Binomial distribution

Published on 30 Mar 2018 - 11:15

score 116 · Answer 3 · 2026-03-29 10:02:11

116

Views

Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$

Published on 29 Mar 2026 - 10:02

score 90 · Answer 4 · 2026-04-01 04:08:41

90

Views

$a < b$ iff $S(a) \leq b$

Published on 01 Apr 2026 - 4:08

score 72 · Answer 5 · 2026-03-27 12:16:55

72

Views

Prove double inequality $2^{1-p}\le x^p+(1-x)^p \le1$

Published on 27 Mar 2026 - 12:16

score 883 · Answer 6 · 2026-03-28 06:23:23

883

Views

Counterexample of Rayleigh Quotient Theorem for specific non-Hermitian matrix

Published on 28 Mar 2026 - 6:23

score 55 · Answer 7 · 2026-03-25 01:20:39

55

Views

How to prove that $\frac 1{q_{n+2}}\leq \left|p_{n}-bq_n\right|$?

Published on 25 Mar 2026 - 1:20

score 158 · Answer 8 · 2026-03-26 01:12:38

158

Views

Given three positive numbers $x,y,z$. Prove that $(x+y-z)(\frac{3}{x+y}-\frac{1}{y+z}-\frac{1}{z+x})\leqq\frac{1}{2}$ .

Published on 26 Mar 2026 - 1:12

score 161 · Answer 9 · 2026-03-30 08:52:57

161

Views

Approximating $\log(n!)$

Published on 30 Mar 2026 - 8:52

score 265 · Answer 10 · 2018-03-31 06:11:09

265

Views

Proving if $\sum\limits_{n=1}^∞\frac1{a_n}<∞$, then $\sum\limits_{n=1}^∞(\frac{na_n}{S_n})^α\frac1{a_n}<∞$

Published on 31 Mar 2018 - 6:11

score 69 · Answer 11 · 2026-03-25 04:41:02

69

Views

Proof verification: $\forall \epsilon\in\Bbb{Q^{+}}\exists x\in\Bbb{Q^{+}}(x^2<2<(x+\epsilon)^2)$

Published on 25 Mar 2026 - 4:41

score 387 · Answer 12 · 2026-03-22 21:32:50

387

Views

Russian MO 2004 $\sqrt{a} + \sqrt{b} + \sqrt{c} \geq ab + bc + ca$

Published on 22 Mar 2026 - 21:32

score 55 · Answer 13 · 2026-03-25 03:01:23

55

Views

Proof related to monotone functions and induction

Published on 25 Mar 2026 - 3:01

score 173 · Answer 14 · 2018-03-31 17:55:11

173

Views

How to find intersection of sets using Archimedean principle?

Published on 31 Mar 2018 - 17:55

score 153 · Answer 15 · 2018-03-31 18:15:21

153

Views

Solve the inequality $\sqrt{\frac{4x-1}{x-a}}>a$

Published on 31 Mar 2018 - 18:15

List Question

If $n\in \mathbb{N},$ then $(1-1/2) (1-1/4)(1-1/8)(1-1/16)...(1-1/2^n)\geq 1/4+1/2^{n+1}.$

Inequality with Binomial distribution

Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$

$a < b$ iff $S(a) \leq b$

Prove double inequality $2^{1-p}\le x^p+(1-x)^p \le1$

Counterexample of Rayleigh Quotient Theorem for specific non-Hermitian matrix

How to prove that $\frac 1{q_{n+2}}\leq \left|p_{n}-bq_n\right|$?

Given three positive numbers $x,y,z$. Prove that $(x+y-z)(\frac{3}{x+y}-\frac{1}{y+z}-\frac{1}{z+x})\leqq\frac{1}{2}$ .

Approximating $\log(n!)$

Proving if $\sum\limits_{n=1}^∞\frac1{a_n}<∞$, then $\sum\limits_{n=1}^∞(\frac{na_n}{S_n})^α\frac1{a_n}<∞$

Proof verification: $\forall \epsilon\in\Bbb{Q^{+}}\exists x\in\Bbb{Q^{+}}(x^2<2<(x+\epsilon)^2)$

Russian MO 2004 $\sqrt{a} + \sqrt{b} + \sqrt{c} \geq ab + bc + ca$

Proof related to monotone functions and induction

How to find intersection of sets using Archimedean principle?

Solve the inequality $\sqrt{\frac{4x-1}{x-a}}>a$

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