List questions from nested-radicals

Published on 23 Apr 2015 - 20:44

1.9k

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Irrationality of $\sqrt{2\sqrt{3\sqrt{4\cdots}}}$

Published on 26 Mar 2026 - 16:05

635

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Is there an exact term for $\sqrt{2+\sqrt{4+\sqrt{8+\dots}}}$

Published on 09 May 2015 - 15:26

191

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Recurring Nested Radical of $0$

Published on 13 May 2015 - 23:48

1k

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How to find this limit and prove it rigorously: $\sqrt{2 + \sqrt{2+\sqrt{2+\sqrt2...)}}}$?

Published on 19 Jun 2015 - 3:43

7.7k

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Find the value of $\sqrt{6+\sqrt{6+\sqrt{6+\dots}}}$

Published on 23 Jun 2015 - 11:28

460

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Limit of $\{a_n\}$, where $a_{n+1} = \sqrt{2+a_n}$

Published on 01 Jul 2015 - 3:42

276

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Closed form for $\sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+...}}}$

Published on 02 Jul 2015 - 21:17

717

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Find the value of $x$ such that $\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-x}}}}=x$

Published on 05 Jul 2015 - 23:01

925

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Find sum of a finite nested radical $ \sqrt{2012+\sqrt{2012+\sqrt{2012+\cdots}}} $ 2012 times

Published on 09 Jul 2015 - 15:34

88

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Evaluating function

Published on 09 Jul 2015 - 21:07

415

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Infinite derivative of nested radicals

Published on 12 Jul 2015 - 16:09

614

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How is Ramanujan's recurrence relation for his nested radical solved?

Published on 13 Jul 2015 - 20:08

90

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Incorrect proposal to dealing with nested radicals?

Published on 16 Jul 2015 - 20:57

389

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Infinitely nested radical problem?

Published on 23 Jul 2015 - 20:05

List Question

Proving $\sqrt{1+\sqrt{2+\cdots+\sqrt{n}}} < 3$ for $n\geq 1$ by induction

Irrationality of $\sqrt{2\sqrt{3\sqrt{4\cdots}}}$

Is there an exact term for $\sqrt{2+\sqrt{4+\sqrt{8+\dots}}}$

Recurring Nested Radical of $0$

How to find this limit and prove it rigorously: $\sqrt{2 + \sqrt{2+\sqrt{2+\sqrt2...)}}}$?

Find the value of $\sqrt{6+\sqrt{6+\sqrt{6+\dots}}}$

Limit of $\{a_n\}$, where $a_{n+1} = \sqrt{2+a_n}$

Closed form for $\sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+...}}}$

Find the value of $x$ such that $\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-x}}}}=x$

Find sum of a finite nested radical $ \sqrt{2012+\sqrt{2012+\sqrt{2012+\cdots}}} $ 2012 times

Evaluating function

Infinite derivative of nested radicals

How is Ramanujan's recurrence relation for his nested radical solved?

Incorrect proposal to dealing with nested radicals?

Infinitely nested radical problem?

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