Question

Given three postive numbers $a,b,c$ so that $a+b+c=3$. Prove that $\sum\frac{1}{a}\geqq (\frac{1}{2}+\frac{5\sqrt{3}}{18})(\!a^{2}+b^{2}+c^{2}\!)$ .

score 203 · Answer 1 · 2026-03-25 06:06:55

203

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Given three postive numbers $a,b,c$ so that $a+b+c=3$. Prove that $\sum\frac{1}{a}\geqq (\frac{1}{2}+\frac{5\sqrt{3}}{18})(\!a^{2}+b^{2}+c^{2}\!)$ .

Published on 25 Mar 2026 - 6:06

score 43 · Answer 2 · 2026-03-16 21:05:42

43

Views

Question about the Gamma function

Published on 16 Mar 2026 - 21:05

score 68 · Answer 3 · 2019-04-18 02:20:47

68

Views

What constant $c$ will make $ \sum_{k=2}^{N}c^{\frac{1}{k\log k}}=N ?$

Published on 18 Apr 2019 - 2:20

score 837 · Answer 4 · 2026-02-23 03:44:44

837

Views

Inverse Laplace Transform - Pulling out the constant

Published on 23 Feb 2026 - 3:44

score 374 · Answer 5 · 2019-04-20 20:10:07

374

Views

Differential Equation by Minimization

Published on 20 Apr 2019 - 20:10

score 313 · Answer 6 · 2019-04-25 15:00:32

313

Views

Proof of the existence of the Ramanujan–Soldner constant

Published on 25 Apr 2019 - 15:00

score 566 · Answer 7 · 2019-04-27 05:38:33

566

Views

What's a good approximation to the zeros of the cosine integral?

Published on 27 Apr 2019 - 5:38

score 59 · Answer 8 · 2019-04-27 11:53:13

59

Views

For what constant $c$ does Struve function $\mathbf{H}_1(x) = c$ have infinitely many roots?

Published on 27 Apr 2019 - 11:53

score 219 · Answer 9 · 2026-03-25 06:13:08

219

Views

Prove that $k=0$ is the only $constant$ so $(\sum\limits_{cyc}a^{3}-\sum\limits_{cyc}a^{2}b)-k(a-b)(a-c)(b+c)\geqq0$ .

Published on 25 Mar 2026 - 6:13

score 51 · Answer 10 · 2019-05-17 07:35:54

51

Views

Determine a Constant

Published on 17 May 2019 - 7:35

score 221 · Answer 11 · 2019-05-22 11:38:52

221

Views

Given three positive numbers $a,b,c$ so that $a\leqq b\leqq c$. Prove that $\sum\limits_{cyc}\frac{a+1.4b}{1.4a+b}\geqq 3$ .

Published on 22 May 2019 - 11:38

score 1.3k · Answer 12 · 2019-06-12 07:39:51

1.3k

Views

List of integrals or series for Gieseking's constant $\rm{Cl}_2\big(\tfrac{\pi}3\big)$?

Published on 12 Jun 2019 - 7:39

score 74 · Answer 13 · 2026-03-25 01:18:39

74

Views

An infinite family of BBP type formulas for Gieseking's constant $\kappa = \rm{Cl}_2\left(\frac\pi3\right)$?

Published on 25 Mar 2026 - 1:18

score 772 · Answer 14 · 2026-03-25 01:20:26

772

Views

Prove $x+ y+ z= 3,\,x^{\,2}+ y^{\,2}+ z^{\,2}= 9\,\therefore\,y- x\leqq 2\sqrt{3}$ .

Published on 25 Mar 2026 - 1:20

score 2.2k · Answer 15 · 2019-06-23 02:06:08

2.2k

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Diagonals of Pascal's Triangle

Published on 23 Jun 2019 - 2:06

List Question

Given three postive numbers $a,b,c$ so that $a+b+c=3$. Prove that $\sum\frac{1}{a}\geqq (\frac{1}{2}+\frac{5\sqrt{3}}{18})(\!a^{2}+b^{2}+c^{2}\!)$ .

Question about the Gamma function

What constant $c$ will make $ \sum_{k=2}^{N}c^{\frac{1}{k\log k}}=N ?$

Inverse Laplace Transform - Pulling out the constant

Differential Equation by Minimization

Proof of the existence of the Ramanujan–Soldner constant

What's a good approximation to the zeros of the cosine integral?

For what constant $c$ does Struve function $\mathbf{H}_1(x) = c$ have infinitely many roots?

Prove that $k=0$ is the only $constant$ so $(\sum\limits_{cyc}a^{3}-\sum\limits_{cyc}a^{2}b)-k(a-b)(a-c)(b+c)\geqq0$ .

Determine a Constant

Given three positive numbers $a,b,c$ so that $a\leqq b\leqq c$. Prove that $\sum\limits_{cyc}\frac{a+1.4b}{1.4a+b}\geqq 3$ .

List of integrals or series for Gieseking's constant $\rm{Cl}_2\big(\tfrac{\pi}3\big)$?

An infinite family of BBP type formulas for Gieseking's constant $\kappa = \rm{Cl}_2\left(\frac\pi3\right)$?

Prove $x+ y+ z= 3,\,x^{\,2}+ y^{\,2}+ z^{\,2}= 9\,\therefore\,y- x\leqq 2\sqrt{3}$ .

Diagonals of Pascal's Triangle

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