Question

Find $\lim_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\sqrt[4]{4+\ldots+\sqrt[n]{n}}}}$

score 374 · Answer 1 · 2016-05-10 01:24:34

374

Views

Find $\lim_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\sqrt[4]{4+\ldots+\sqrt[n]{n}}}}$

Published on 10 May 2016 - 1:24

score 701 · Answer 2 · 2016-05-12 07:23:09

701

Views

Find $\sqrt{4+\sqrt[3]{4+\sqrt[4]{4+\sqrt[5]{4+\cdots}}}}$

Published on 12 May 2016 - 7:23

score 194 · Answer 3 · 2016-05-12 09:41:30

194

Views

Calculating $\sqrt[3]{\sqrt 5 +2}-\sqrt[3]{\sqrt 5 -2}$

Published on 12 May 2016 - 9:41

score 326 · Answer 4 · 2016-05-18 12:49:40

326

Views

Simplify $\frac{1}{\sqrt{4+2\sqrt{3}} - \sqrt{4-2\sqrt{3}}}$

Published on 18 May 2016 - 12:49

score 1.7k · Answer 5 · 2016-05-19 15:50:09

1.7k

Views

Why is $5\tan(54^\circ) = \sqrt{25 + 10\sqrt{5}}$ and $\tan\left(\frac{\pi}{5}\right) = \sqrt{5 - 2\sqrt{5}}$?

Published on 19 May 2016 - 15:50

score 62 · Answer 6 · 2016-05-19 17:23:19

62

Views

Prove $\frac{\sqrt[n]k+1}{\sqrt[n]k-1}=\frac{2}{k-1}\left(\frac{k+1}{2}+\sum_{j=1}^{n-1}\sqrt[n]{k^j}\right)$

Published on 19 May 2016 - 17:23

score 155 · Answer 7 · 2016-05-23 18:48:57

155

Views

About a curious nested radical representation for $\cos 1^\circ$

Published on 23 May 2016 - 18:48

score 522 · Answer 8 · 2016-05-28 19:17:41

522

Views

Simplify $\sqrt[3]{\sqrt[3]{A}-B}$ to $\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}$

Published on 28 May 2016 - 19:17

score 185 · Answer 9 · 2016-05-30 20:44:34

185

Views

On the convergence of a more complex iterated radical

Published on 30 May 2016 - 20:44

score 122 · Answer 10 · 2016-06-02 03:21:55

122

Views

Problem with Denesting Radical Relations

Published on 02 Jun 2016 - 3:21

score 140 · Answer 11 · 2016-06-05 21:39:23

140

Views

How to prove the following curious nested radical identity?

Published on 05 Jun 2016 - 21:39

score 134 · Answer 12 · 2016-06-06 16:01:04

134

Views

Solving a radical to find the value

Published on 06 Jun 2016 - 16:01

score 287 · Answer 13 · 2016-06-09 15:41:27

287

Views

Solve the equation $\lim_{n\to\infty}\sqrt{1+\sqrt{x+\sqrt{x^2+\dots+\sqrt{x^n}}}}=2$

Published on 09 Jun 2016 - 15:41

score 1k · Answer 14 · 2026-03-26 23:10:39

1k

Views

How to find $\lim_{n \to \infty} \int_0^1 \cdots \int_0^1 \sqrt{x_1+\sqrt{x_2+\sqrt{\dots+\sqrt{x_n}}}}dx_1 dx_2\dots dx_n$

Published on 26 Mar 2026 - 23:10

score 29.5k · Answer 15 · 2016-06-16 13:00:43

29.5k

Views

How do you simplify this square root of sum: $\sqrt{7+4\sqrt3}$?

Published on 16 Jun 2016 - 13:00

List Question

Find $\lim_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\sqrt[4]{4+\ldots+\sqrt[n]{n}}}}$

Find $\sqrt{4+\sqrt[3]{4+\sqrt[4]{4+\sqrt[5]{4+\cdots}}}}$

Calculating $\sqrt[3]{\sqrt 5 +2}-\sqrt[3]{\sqrt 5 -2}$

Simplify $\frac{1}{\sqrt{4+2\sqrt{3}} - \sqrt{4-2\sqrt{3}}}$

Why is $5\tan(54^\circ) = \sqrt{25 + 10\sqrt{5}}$ and $\tan\left(\frac{\pi}{5}\right) = \sqrt{5 - 2\sqrt{5}}$?

Prove $\frac{\sqrt[n]k+1}{\sqrt[n]k-1}=\frac{2}{k-1}\left(\frac{k+1}{2}+\sum_{j=1}^{n-1}\sqrt[n]{k^j}\right)$

About a curious nested radical representation for $\cos 1^\circ$

Simplify $\sqrt[3]{\sqrt[3]{A}-B}$ to $\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}$

On the convergence of a more complex iterated radical

Problem with Denesting Radical Relations

How to prove the following curious nested radical identity?

Solving a radical to find the value

Solve the equation $\lim_{n\to\infty}\sqrt{1+\sqrt{x+\sqrt{x^2+\dots+\sqrt{x^n}}}}=2$

How to find $\lim_{n \to \infty} \int_0^1 \cdots \int_0^1 \sqrt{x_1+\sqrt{x_2+\sqrt{\dots+\sqrt{x_n}}}}dx_1 dx_2\dots dx_n$

How do you simplify this square root of sum: $\sqrt{7+4\sqrt3}$?

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