Question

polynomial nesting technique for $f(x)=\sqrt{x^2+1}-x$

score 113 · Answer 1 · 2021-10-20 21:59:13

113

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polynomial nesting technique for $f(x)=\sqrt{x^2+1}-x$

Published on 20 Oct 2021 - 21:59

score 66 · Answer 2 · 2021-11-08 11:40:06

66

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Truncation error for $ S = \sum_{m=0}^\infty \frac{\beta^m}{m!}a^{-\frac{m+1}{k}}\Gamma\left(\frac{m+1}{k}\right)$

Published on 08 Nov 2021 - 11:40

score 125 · Answer 3 · 2021-11-15 21:36:56

125

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Showing that $\sqrt{2+\sqrt3}=\frac{\sqrt2+\sqrt6}{2}$

Published on 15 Nov 2021 - 21:36

score 77 · Answer 4 · 2021-11-27 11:14:21

77

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A nested radical

Published on 27 Nov 2021 - 11:14

score 116 · Answer 5 · 2021-12-04 03:23:26

116

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What is the result of $\sqrt{-\frac{1}{4}+\sqrt{-\frac{1}{4}+\sqrt{-\frac{1}{4}+\sqrt{-\frac{1}{4}+...}}}}$

Published on 04 Dec 2021 - 3:23

score 94 · Answer 6 · 2021-12-04 11:35:12

94

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Finding a root of a degree 5 polynomial

Published on 04 Dec 2021 - 11:35

score 100 · Answer 7 · 2021-12-12 19:06:51

100

Views

Nested sine and cosine half angle formulas

Published on 12 Dec 2021 - 19:06

score 92 · Answer 8 · 2021-12-18 18:40:37

92

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Is there a general form for infinite nested radicals of degreen n?

Published on 18 Dec 2021 - 18:40

score 227 · Answer 9 · 2021-12-28 04:39:14

227

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Recursive sequence relationship with repeating nested radicals

Published on 28 Dec 2021 - 4:39

score 34 · Answer 10 · 2026-02-27 03:06:14

34

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Convergence of Sequence of functions with nested radicals.

Published on 27 Feb 2026 - 3:06

score 110 · Answer 11 · 2026-03-27 01:47:38

110

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How does $ f(x)=\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}. x \ge1 $ produce a piecewise function with an interval that is a constant fucntion?

Published on 27 Mar 2026 - 1:47

score 147 · Answer 12 · 2022-04-05 06:06:11

147

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Looking for 2 nested radicals neither of which denest but their sum DOES denest.

Published on 05 Apr 2022 - 6:06

score 131 · Answer 13 · 2022-04-06 08:14:26

131

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Solving $3 + \sqrt{3^2 + \sqrt{3^4 + \sqrt{3^8 + \sqrt{3^{16} + ...}}}}$

Published on 06 Apr 2022 - 8:14

score 602 · Answer 14 · 2026-02-24 10:16:07

602

Views

A Proof with no words that $\sqrt{2+\sqrt{2+\sqrt{2+\cdots}}}=2$

Published on 24 Feb 2026 - 10:16

score 144 · Answer 15 · 2022-05-09 00:49:32

144

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General formula for the upper bound of pi involving nested square roots (circumscribed perimeters of regular polygons)

Published on 09 May 2022 - 0:49

List Question

polynomial nesting technique for $f(x)=\sqrt{x^2+1}-x$

Truncation error for $ S = \sum_{m=0}^\infty \frac{\beta^m}{m!}a^{-\frac{m+1}{k}}\Gamma\left(\frac{m+1}{k}\right)$

Showing that $\sqrt{2+\sqrt3}=\frac{\sqrt2+\sqrt6}{2}$

A nested radical

What is the result of $\sqrt{-\frac{1}{4}+\sqrt{-\frac{1}{4}+\sqrt{-\frac{1}{4}+\sqrt{-\frac{1}{4}+...}}}}$

Finding a root of a degree 5 polynomial

Nested sine and cosine half angle formulas

Is there a general form for infinite nested radicals of degreen n?

Recursive sequence relationship with repeating nested radicals

Convergence of Sequence of functions with nested radicals.

How does $ f(x)=\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}. x \ge1 $ produce a piecewise function with an interval that is a constant fucntion?

Looking for 2 nested radicals neither of which denest but their sum DOES denest.

Solving $3 + \sqrt{3^2 + \sqrt{3^4 + \sqrt{3^8 + \sqrt{3^{16} + ...}}}}$

A Proof with no words that $\sqrt{2+\sqrt{2+\sqrt{2+\cdots}}}=2$

General formula for the upper bound of pi involving nested square roots (circumscribed perimeters of regular polygons)

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