Question

On Ramanujan's approximation, $n!\sim \sqrt{\pi}\big(\frac ne\big)^n\sqrt [6]{(2n)^3+(2n)^2+n+\frac 1{30}}$

score 533 · Answer 1 · 2026-04-01 02:50:19

533

Views

On Ramanujan's approximation, $n!\sim \sqrt{\pi}\big(\frac ne\big)^n\sqrt [6]{(2n)^3+(2n)^2+n+\frac 1{30}}$

Published on 01 Apr 2026 - 2:50

score 208 · Answer 2 · 2026-03-30 07:09:13

208

Views

Show that $\lim _{x\to \infty }\left(\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}\right) =1/2$

Published on 30 Mar 2026 - 7:09

score 854 · Answer 3 · 2026-03-28 13:38:27

854

Views

When does $\sqrt{x+\sqrt{x+1+\sqrt{x+2+...}}}=0$?

Published on 28 Mar 2026 - 13:38

score 270 · Answer 4 · 2020-04-23 11:41:55

270

Views

What is the role played by the difference of the two roots in solving a quadratic equation?

Published on 23 Apr 2020 - 11:41

score 30 · Answer 5 · 2020-04-23 12:32:19

30

Views

What can a translation of $y=x-e$ do to bring a polynomial into a depressed form?

Published on 23 Apr 2020 - 12:32

score 35 · Answer 6 · 2020-04-23 20:41:14

35

Views

What can a translation of a polynomial do to bring the equation into a nicer form?

Published on 23 Apr 2020 - 20:41

score 24 · Answer 7 · 2026-03-27 20:21:30

24

Views

What role do symmetries play in solving a quadratic and higher degree polynomial?

Published on 27 Mar 2026 - 20:21

score 65 · Answer 8 · 2020-04-24 15:43:28

65

Views

How can I show that $uv = 5 + 2 i \sqrt{3}$ implies that either $u$ or $v$ is $1$ or $-1$?

Published on 24 Apr 2020 - 15:43

score 66 · Answer 9 · 2026-03-29 16:38:56

66

Views

Why Test for positive and negatives in a Square Root of a Squared Function?

Published on 29 Mar 2026 - 16:38

score 70 · Answer 10 · 2026-03-26 22:19:15

70

Views

Specifying algebraic numbers over $\mathbb{Q}$ using GAP

Published on 26 Mar 2026 - 22:19

score 126 · Answer 11 · 2026-03-28 16:58:11

126

Views

Proof $\frac{-\sqrt{2 - \sqrt{2 - \sqrt{2}}}}{\sqrt2} + \frac{\sqrt{2 + \sqrt2}}{\sqrt2 \sqrt{2 - \sqrt{2 - \sqrt2}}} =\sqrt{2-\sqrt{2+\sqrt2}}$

Published on 28 Mar 2026 - 16:58

score 119 · Answer 12 · 2026-03-25 15:53:37

119

Views

On the asymptotics of $\sum_{k=1}^{n^2} \{\sqrt{k}\} $

Published on 25 Mar 2026 - 15:53

score 115 · Answer 13 · 2020-04-26 17:20:22

115

Views

Checking if $\mathbb{Q}(5^{1/10},e^{\pi i/5})=\mathbb{Q}(5^{1/10},i)$

Published on 26 Apr 2020 - 17:20

score 58 · Answer 14 · 2020-04-28 22:02:54

58

Views

Simplifying $\frac{-8+\sqrt{48}}{8}$ to $\frac{-2+\sqrt{3}}{2}$

Published on 28 Apr 2020 - 22:02

score 103 · Answer 15 · 2026-03-29 16:33:58

103

Views

Squaring the square root of a negative number

Published on 29 Mar 2026 - 16:33

List Question

On Ramanujan's approximation, $n!\sim \sqrt{\pi}\big(\frac ne\big)^n\sqrt [6]{(2n)^3+(2n)^2+n+\frac 1{30}}$

Show that $\lim _{x\to \infty }\left(\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}\right) =1/2$

When does $\sqrt{x+\sqrt{x+1+\sqrt{x+2+...}}}=0$?

What is the role played by the difference of the two roots in solving a quadratic equation?

What can a translation of $y=x-e$ do to bring a polynomial into a depressed form?

What can a translation of a polynomial do to bring the equation into a nicer form?

What role do symmetries play in solving a quadratic and higher degree polynomial?

How can I show that $uv = 5 + 2 i \sqrt{3}$ implies that either $u$ or $v$ is $1$ or $-1$?

Why Test for positive and negatives in a Square Root of a Squared Function?

Specifying algebraic numbers over $\mathbb{Q}$ using GAP

Proof $\frac{-\sqrt{2 - \sqrt{2 - \sqrt{2}}}}{\sqrt2} + \frac{\sqrt{2 + \sqrt2}}{\sqrt2 \sqrt{2 - \sqrt{2 - \sqrt2}}} =\sqrt{2-\sqrt{2+\sqrt2}}$

On the asymptotics of $\sum_{k=1}^{n^2} \{\sqrt{k}\} $

Checking if $\mathbb{Q}(5^{1/10},e^{\pi i/5})=\mathbb{Q}(5^{1/10},i)$

Simplifying $\frac{-8+\sqrt{48}}{8}$ to $\frac{-2+\sqrt{3}}{2}$

Squaring the square root of a negative number

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