Question

Interpolating function for a nested radical $y_x=\sqrt{a+y_{x-1}}$

score 249 · Answer 1 · 2026-03-28 21:50:39

249

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Interpolating function for a nested radical $y_x=\sqrt{a+y_{x-1}}$

Published on 28 Mar 2026 - 21:50

score 889 · Answer 2 · 2017-01-19 20:44:26

889

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What is $1+(2+(3+(4+...+(n-1+n^{1/n})^{1/(n-1)}) ...)^{1/4})^{1/3})^{1/2}$ equal to?

Published on 19 Jan 2017 - 20:44

score 125 · Answer 3 · 2017-01-19 21:50:11

125

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Is $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ rational?

Published on 19 Jan 2017 - 21:50

score 144 · Answer 4 · 2017-01-24 18:01:12

144

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Infinitely nested radical indexed by powers of two

Published on 24 Jan 2017 - 18:01

score 129 · Answer 5 · 2017-01-28 12:16:43

129

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Solve for x (quadratic equation)

Published on 28 Jan 2017 - 12:16

score 214 · Answer 6 · 2017-01-31 21:14:04

214

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The $n$th term of this infinitely nested radical sequence

Published on 31 Jan 2017 - 21:14

score 78 · Answer 7 · 2017-02-02 17:15:26

78

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Derivative and Integral of $f(x+f(x+f(x+...)))$ and other interesting features

Published on 02 Feb 2017 - 17:15

score 1.5k · Answer 8 · 2017-02-06 21:06:36

1.5k

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Is there an explicit formula that gives the value of $\sqrt{2+\sqrt{2+\sqrt{2+\cdots}}}$ for $n$ square roots?

Published on 06 Feb 2017 - 21:06

score 165 · Answer 9 · 2017-02-13 20:26:13

165

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How to solve for $x$ algebraically, given that $x^2 = 4- \sqrt{12}$

Published on 13 Feb 2017 - 20:26

score 205 · Answer 10 · 2017-02-18 14:25:56

205

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Find the greatest integer not exceeding $A$ if $A = \sqrt{x^2+\sqrt{4x^2+\sqrt{16x^2+\sqrt{100x^2+39x+\sqrt{3}}}}}$ and $x=20062007$.

Published on 18 Feb 2017 - 14:25

score 3.6k · Answer 11 · 2017-02-19 13:37:08

3.6k

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A formula for $\sin(\pi/2^n)$

Published on 19 Feb 2017 - 13:37

score 56 · Answer 12 · 2017-02-19 14:08:06

56

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Asymptotics to the sequence leading up to an infinitely nested radical

Published on 19 Feb 2017 - 14:08

score 178 · Answer 13 · 2026-03-27 23:28:05

178

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How can I show that this complicated expression with square and cube roots reduces to the value 7?

Published on 27 Mar 2026 - 23:28

score 224 · Answer 14 · 2017-02-28 20:51:19

224

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Show that $\sqrt{2-\sqrt{3}}=\frac{1}{2}(\sqrt{6}-\sqrt{2})$

Published on 28 Feb 2017 - 20:51

score 153 · Answer 15 · 2017-03-05 17:54:15

153

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Prove that $\lim_{n \to \infty}{\sqrt{n+\sqrt{n}}} = \lim_{n \to \infty}{\sqrt{n}}$

Published on 05 Mar 2017 - 17:54

List Question

Interpolating function for a nested radical $y_x=\sqrt{a+y_{x-1}}$

What is $1+(2+(3+(4+...+(n-1+n^{1/n})^{1/(n-1)}) ...)^{1/4})^{1/3})^{1/2}$ equal to?

Is $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ rational?

Infinitely nested radical indexed by powers of two

Solve for x (quadratic equation)

The $n$th term of this infinitely nested radical sequence

Derivative and Integral of $f(x+f(x+f(x+...)))$ and other interesting features

Is there an explicit formula that gives the value of $\sqrt{2+\sqrt{2+\sqrt{2+\cdots}}}$ for $n$ square roots?

How to solve for $x$ algebraically, given that $x^2 = 4- \sqrt{12}$

Find the greatest integer not exceeding $A$ if $A = \sqrt{x^2+\sqrt{4x^2+\sqrt{16x^2+\sqrt{100x^2+39x+\sqrt{3}}}}}$ and $x=20062007$.

A formula for $\sin(\pi/2^n)$

Asymptotics to the sequence leading up to an infinitely nested radical

How can I show that this complicated expression with square and cube roots reduces to the value 7?

Show that $\sqrt{2-\sqrt{3}}=\frac{1}{2}(\sqrt{6}-\sqrt{2})$

Prove that $\lim_{n \to \infty}{\sqrt{n+\sqrt{n}}} = \lim_{n \to \infty}{\sqrt{n}}$

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