Question

Representing $\cos(\frac{π}{11})$ as cyclic infinite nested square roots of $2$

score 191 · Answer 1 · 2020-10-04 18:07:16

191

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Representing $\cos(\frac{π}{11})$ as cyclic infinite nested square roots of $2$

Published on 04 Oct 2020 - 18:07

score 167 · Answer 2 · 2020-10-06 05:56:29

167

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Infinite Nested Square Root, Prove or disprove that there is at least one real number satisfy

Published on 06 Oct 2020 - 5:56

score 326 · Answer 3 · 2020-10-06 06:52:29

326

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Prove that $\frac{a}{1+a^2}+\frac{b}{1+a^2+b^2}+\frac{c}{1+a^2+b^2+c^2}+\frac{d}{1+a^2+b^2+c^2+d^2}\leq\frac{3}{2}$

Published on 06 Oct 2020 - 6:52

score 114 · Answer 4 · 2020-10-08 16:47:07

114

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Does the sequence $t_n=\sqrt{a_1+\sqrt{a_2+\cdots+\sqrt{a_n}}} (a_k>0,k=1,2,\cdots)$ converge?

Published on 08 Oct 2020 - 16:47

score 224 · Answer 5 · 2026-03-26 11:47:53

224

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Rationalize the denominator of $2\over{2 - \sqrt[4]{2}}$?

Published on 26 Mar 2026 - 11:47

score 1k · Answer 6 · 2020-10-15 19:48:15

1k

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Taylor series expansion and value of cosine angle

Published on 15 Oct 2020 - 19:48

score 190 · Answer 7 · 2020-10-18 16:22:54

190

Views

Nested radicals like Ramanujan's infinite radicals

Published on 18 Oct 2020 - 16:22

score 238 · Answer 8 · 2020-10-25 00:12:51

238

Views

How to denest $\sqrt[3]{\sqrt[3]{2}-1}=\sqrt[3]{\frac19}-\sqrt[3]{\frac29}+\sqrt[3]{\frac49}$ from scratch?

Published on 25 Oct 2020 - 0:12

score 186 · Answer 9 · 2020-10-25 17:35:25

186

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How to prove $f(x)=\sqrt{x+\sqrt{x+\sqrt{x}}}$ is differentiable?

Published on 25 Oct 2020 - 17:35

score 179 · Answer 10 · 2020-11-05 09:25:02

179

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Find derivative of $f(x)=\tan^2x \sqrt{\tan x\sqrt[3]{\tan x\sqrt[4]{\tan x...}}}$

Published on 05 Nov 2020 - 9:25

score 194 · Answer 11 · 2020-11-10 21:43:24

194

Views

Sum of cube roots of two conjugate quadratic integers makes an integer.

Published on 10 Nov 2020 - 21:43

score 97 · Answer 12 · 2020-11-21 00:36:16

97

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Solve the inequality $\sqrt[3]{1+(3+x)\sqrt{x}+3x} - \sqrt[3]{1-(3+x)\sqrt{x}+3x} > x + a$

Published on 21 Nov 2020 - 0:36

score 453 · Answer 13 · 2020-11-22 11:15:41

453

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Infinite ways to represent $\pi$ as product of nested square roots of $2$ and $2^n$ and odd numbers

Published on 22 Nov 2020 - 11:15

score 210 · Answer 14 · 2020-11-28 18:42:51

210

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Solving $\sqrt{2+\sqrt{2-\sqrt{2+x}}} = x$.

Published on 28 Nov 2020 - 18:42

score 486 · Answer 15 · 2020-12-03 13:29:06

486

Views

Interesting infinite nested square roots of 2 for $2\cos1°$ and $2\sin1°$

Published on 03 Dec 2020 - 13:29

List Question

Representing $\cos(\frac{π}{11})$ as cyclic infinite nested square roots of $2$

Infinite Nested Square Root, Prove or disprove that there is at least one real number satisfy

Prove that $\frac{a}{1+a^2}+\frac{b}{1+a^2+b^2}+\frac{c}{1+a^2+b^2+c^2}+\frac{d}{1+a^2+b^2+c^2+d^2}\leq\frac{3}{2}$

Does the sequence $t_n=\sqrt{a_1+\sqrt{a_2+\cdots+\sqrt{a_n}}} (a_k>0,k=1,2,\cdots)$ converge?

Rationalize the denominator of $2\over{2 - \sqrt[4]{2}}$?

Taylor series expansion and value of cosine angle

Nested radicals like Ramanujan's infinite radicals

How to denest $\sqrt[3]{\sqrt[3]{2}-1}=\sqrt[3]{\frac19}-\sqrt[3]{\frac29}+\sqrt[3]{\frac49}$ from scratch?

How to prove $f(x)=\sqrt{x+\sqrt{x+\sqrt{x}}}$ is differentiable?

Find derivative of $f(x)=\tan^2x \sqrt{\tan x\sqrt[3]{\tan x\sqrt[4]{\tan x...}}}$

Sum of cube roots of two conjugate quadratic integers makes an integer.

Solve the inequality $\sqrt[3]{1+(3+x)\sqrt{x}+3x} - \sqrt[3]{1-(3+x)\sqrt{x}+3x} > x + a$

Infinite ways to represent $\pi$ as product of nested square roots of $2$ and $2^n$ and odd numbers

Solving $\sqrt{2+\sqrt{2-\sqrt{2+x}}} = x$.

Interesting infinite nested square roots of 2 for $2\cos1°$ and $2\sin1°$

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