Question

Improvements of Dusart's lower bound for $ e^\gamma \log x \prod_{p\le x} \frac{p-1}{p}$.

score 253 · Answer 1 · 2014-12-02 14:06:24

253

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Improvements of Dusart's lower bound for $ e^\gamma \log x \prod_{p\le x} \frac{p-1}{p}$.

Published on 02 Dec 2014 - 14:06

score 111 · Answer 2 · 2026-03-25 17:35:40

111

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Summation verification

Published on 25 Mar 2026 - 17:35

score 1.7k · Answer 3 · 2014-12-07 04:02:07

1.7k

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Is the term "telescoping product" well known?

Published on 07 Dec 2014 - 4:02

score 447 · Answer 4 · 2014-12-07 19:52:15

447

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Two (strictly related) proofs by induction of inequalities.

Published on 07 Dec 2014 - 19:52

score 131 · Answer 5 · 2014-12-13 16:01:06

131

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Study the convergence of $\sum_{n=1}^{\infty}{\prod_{k=1}^{n}{\sin (k)}}$

Published on 13 Dec 2014 - 16:01

score 952 · Answer 6 · 2026-03-29 08:18:23

952

Views

Factorial inequality $2!\,4!\,6!\cdots (2n)!\geq\left((n+1)!\right)^n$ using induction

Published on 29 Mar 2026 - 8:18

score 571 · Answer 7 · 2014-12-18 14:24:55

571

Views

Generalized Holder Inequality

Published on 18 Dec 2014 - 14:24

score 110 · Answer 8 · 2014-12-20 10:31:09

110

Views

Evaluate this infinite product involving $a_k$

Published on 20 Dec 2014 - 10:31

score 819 · Answer 9 · 2014-12-21 06:07:20

819

Views

How to prove that a product of two complete residue system is not a complete residue system?

Published on 21 Dec 2014 - 6:07

score 649 · Answer 10 · 2026-03-25 22:26:44

649

Views

Preferred way to write elements of the direct sum of vector spaces

Published on 25 Mar 2026 - 22:26

score 231 · Answer 11 · 2014-12-23 00:54:35

231

Views

Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.

Published on 23 Dec 2014 - 0:54

score 66 · Answer 12 · 2014-12-23 22:44:54

66

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Proving that $ \prod_{i=1}^{n} (1 + a_{i}) \ge \left(1 + \prod_{i=1}^{n} a_{i}^{1/n} \right)^{n} $

Published on 23 Dec 2014 - 22:44

score 207 · Answer 13 · 2026-03-29 08:15:07

207

Views

An inequality for the product $\prod_{k=2}^{n}\cos\frac{\pi }{2^{k}}$

Published on 29 Mar 2026 - 8:15

score 98 · Answer 14 · 2014-12-26 18:12:46

Solve $p_4(x) = x^4 −(2m + 4)x^2 + (m−2)^2 $such that $p_4$ is a product of two non-constant integer-coeficient polynomials

score 234 · Answer 15 · 2026-03-28 01:26:23

234

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Proving the inequality $ \left|\prod_{i=0}^n \left(x - \frac{i}{n}\right)\right| \le \frac{n!}{4n^{n+1}}$

Published on 28 Mar 2026 - 1:26

List Question

Improvements of Dusart's lower bound for $ e^\gamma \log x \prod_{p\le x} \frac{p-1}{p}$.

Summation verification

Is the term "telescoping product" well known?

Two (strictly related) proofs by induction of inequalities.

Study the convergence of $\sum_{n=1}^{\infty}{\prod_{k=1}^{n}{\sin (k)}}$

Factorial inequality $2!\,4!\,6!\cdots (2n)!\geq\left((n+1)!\right)^n$ using induction

Generalized Holder Inequality

Evaluate this infinite product involving $a_k$

How to prove that a product of two complete residue system is not a complete residue system?

Preferred way to write elements of the direct sum of vector spaces

Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.

Proving that $ \prod_{i=1}^{n} (1 + a_{i}) \ge \left(1 + \prod_{i=1}^{n} a_{i}^{1/n} \right)^{n} $

An inequality for the product $\prod_{k=2}^{n}\cos\frac{\pi }{2^{k}}$

Solve $p_4(x) = x^4 −(2m + 4)x^2 + (m−2)^2 $such that $p_4$ is a product of two non-constant integer-coeficient polynomials

Proving the inequality $ \left|\prod_{i=0}^n \left(x - \frac{i}{n}\right)\right| \le \frac{n!}{4n^{n+1}}$

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