Question

Prove the inequality $\sum \limits_{k=1}^n \frac{k+1}{k} \cdot \sum \limits_{k=1}^n \frac{k}{k+1} \le \frac{9}{8}n^2$

score 331 · Answer 1 · 2026-03-25 06:39:15

331

Views

Prove the inequality $\sum \limits_{k=1}^n \frac{k+1}{k} \cdot \sum \limits_{k=1}^n \frac{k}{k+1} \le \frac{9}{8}n^2$

Published on 25 Mar 2026 - 6:39

score 258 · Answer 2 · 2019-08-03 15:46:26

258

Views

Prove $ \left(\sum \limits_{k=1}^n (2k-1)\frac{k+1}{k}\right) \left( \sum \limits_{k=1}^n (2k-1)\frac{k}{k+1}\right) \le \frac{9}{8}n^4$

Published on 03 Aug 2019 - 15:46

score 474 · Answer 3 · 2019-08-03 19:20:26

Interesting four-sum inequality $n^2 \left(\sum \limits_{k=1}^n \frac{k+1}{k}\right) \left( \sum \limits_{k=1}^n \frac{k}{k+1}\right) \ge...$

score 205 · Answer 4 · 2026-03-25 21:48:19

205

Views

Solutions of bivariate cubic Diophantine equation

Published on 25 Mar 2026 - 21:48

score 471 · Answer 5 · 2026-03-25 09:27:36

471

Views

It may be a strengthening form of mean inequality

Published on 25 Mar 2026 - 9:27

score 61 · Answer 6 · 2019-08-05 08:35:57

61

Views

there exsit a real coefficient polynomial $g(x)$ of degree $n$. and for complex numbers $z(|z|=1)$ have $|g(z)|^2=1+|f(z)|^2$

Published on 05 Aug 2019 - 8:35

score 149 · Answer 7 · 2019-08-05 12:39:09

149

Views

Perfect squares of the form $ab^n+c$ and a Diophantine equation

Published on 05 Aug 2019 - 12:39

score 592 · Answer 8 · 2019-08-05 17:31:44

592

Views

Find the number of polynomials $P(x)$ with coefficients $0,1,2,3$ such that $P(2) = n$.

Published on 05 Aug 2019 - 17:31

score 289 · Answer 9 · 2026-03-27 05:38:00

289

Views

Solve $a!b!=a!+b!+c!$ where $a$, $b$ and $c$ are nonnegative integers.

Published on 27 Mar 2026 - 5:38

score 69 · Answer 10 · 2026-03-28 21:27:12

69

Views

Find every $n$: $n^2 + 340 = m^2$

Published on 28 Mar 2026 - 21:27

score 108 · Answer 11 · 2019-08-07 11:23:06

108

Views

Constant function given an inequality

Published on 07 Aug 2019 - 11:23

score 137 · Answer 12 · 2019-08-07 12:11:21

137

Views

Max of $(a-x^2)(b-y^2)(c-z^2)$ when $x+y+z=a+b+c=1$, $x,y,z,a,b,c \geq 0$

Published on 07 Aug 2019 - 12:11

score 136 · Answer 13 · 2026-03-31 04:28:46

136

Views

From $D$ on any side of $\triangle ABC$, drop perpendiculars $DP$, $DQ$ to other sides. Find minimum value of $|PQ|$.

Published on 31 Mar 2026 - 4:28

score 408 · Answer 14 · 2026-03-25 22:11:14

408

Views

Are functions that sum to zero over vertices of similar polygons identically zero?

Published on 25 Mar 2026 - 22:11

score 415 · Answer 15 · 2019-08-10 02:28:43

415

Views

Find four distinct positive integers whose product is divisible by the sum of every pair of them.

Published on 10 Aug 2019 - 2:28

List Question

Prove the inequality $\sum \limits_{k=1}^n \frac{k+1}{k} \cdot \sum \limits_{k=1}^n \frac{k}{k+1} \le \frac{9}{8}n^2$

Prove $ \left(\sum \limits_{k=1}^n (2k-1)\frac{k+1}{k}\right) \left( \sum \limits_{k=1}^n (2k-1)\frac{k}{k+1}\right) \le \frac{9}{8}n^4$

Interesting four-sum inequality $n^2 \left(\sum \limits_{k=1}^n \frac{k+1}{k}\right) \left( \sum \limits_{k=1}^n \frac{k}{k+1}\right) \ge...$

Solutions of bivariate cubic Diophantine equation

It may be a strengthening form of mean inequality

there exsit a real coefficient polynomial $g(x)$ of degree $n$. and for complex numbers $z(|z|=1)$ have $|g(z)|^2=1+|f(z)|^2$

Perfect squares of the form $ab^n+c$ and a Diophantine equation

Find the number of polynomials $P(x)$ with coefficients $0,1,2,3$ such that $P(2) = n$.

Solve $a!b!=a!+b!+c!$ where $a$, $b$ and $c$ are nonnegative integers.

Find every $n$: $n^2 + 340 = m^2$

Constant function given an inequality

Max of $(a-x^2)(b-y^2)(c-z^2)$ when $x+y+z=a+b+c=1$, $x,y,z,a,b,c \geq 0$

From $D$ on any side of $\triangle ABC$, drop perpendiculars $DP$, $DQ$ to other sides. Find minimum value of $|PQ|$.

Are functions that sum to zero over vertices of similar polygons identically zero?

Find four distinct positive integers whose product is divisible by the sum of every pair of them.

Trending Questions

Popular # Hahtags

Popular Questions