Question

Show that series $a_{n+1} = \sqrt{1+\sqrt{a_n}}$ converges

score 4.2k · Answer 1 · 2026-03-28 22:28:16

4.2k

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Show that series $a_{n+1} = \sqrt{1+\sqrt{a_n}}$ converges

Published on 28 Mar 2026 - 22:28

score 397 · Answer 2 · 2016-09-16 00:29:06

397

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Calculate radical expression without a calculator

Published on 16 Sep 2016 - 0:29

score 212 · Answer 3 · 2026-03-26 17:54:00

212

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Prove the inequality $\sqrt{a^2+b^2}+\sqrt{c^2+b^2}+\sqrt{a^2+c^2}<1+\frac{\sqrt2}{2}$

Published on 26 Mar 2026 - 17:54

score 526 · Answer 4 · 2026-03-31 08:52:49

526

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is $\sqrt[n]{n!}$ ever an integer?

Published on 31 Mar 2026 - 8:52

score 713 · Answer 5 · 2016-09-18 21:12:49

713

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When is a radical in its simplest form? Seemingly conflicting answers

Published on 18 Sep 2016 - 21:12

score 137 · Answer 6 · 2026-03-25 20:36:06

137

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How to find $x,y$ : $2^{x^2+y} + 2^{x + y^2} = 128$ , $\sqrt{x} + \sqrt{y} = 2\sqrt{2}$

Published on 25 Mar 2026 - 20:36

score 2.2k · Answer 7 · 2016-09-20 05:23:34

2.2k

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Limit of $n -\sqrt{n^2+2n}$

Published on 20 Sep 2016 - 5:23

score 1.7k · Answer 8 · 2026-03-28 22:24:55

1.7k

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Simplify $\sqrt{1+\sqrt 2}$

Published on 28 Mar 2026 - 22:24

score 70 · Answer 9 · 2016-09-22 18:24:00

70

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What is the sum of x+y?

Published on 22 Sep 2016 - 18:24

score 214 · Answer 10 · 2016-09-22 19:18:50

214

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Finding limit of sequence, done right: $a(n)=\sqrt{n^2+9}-\sqrt{n^2-n+9}$?

Published on 22 Sep 2016 - 19:18

score 10.1k · Answer 11 · 2026-04-01 11:02:23

10.1k

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Prove $\sqrt{3} + \sqrt{5}$ is irrational

Published on 01 Apr 2026 - 11:02

score 767 · Answer 12 · 2016-09-23 18:19:51

767

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Convergence of a series with radicals: $\sum\limits_{n=1}^{\infty}\frac{\sqrt{n+2}-\sqrt{n+1}}{n}$

Published on 23 Sep 2016 - 18:19

score 55 · Answer 13 · 2016-09-25 00:04:28

55

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Please help me understand the steps to simplify this radical

Published on 25 Sep 2016 - 0:04

score 288 · Answer 14 · 2026-03-31 12:01:29

288

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I conjecture this inequality $\sqrt[4]{\frac{(xy+yz+xz)(x^2+y^2+z^2)}{9}}\ge\sqrt[3]{\frac{(x+y)(y+z)(z+x)}{8}}$

Published on 31 Mar 2026 - 12:01

score 1.8k · Answer 15 · 2016-09-26 21:33:54

1.8k

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Please give me the method of writing $\sqrt{33 + 12 \sqrt 6}$ in the form $a + b \sqrt c$

Published on 26 Sep 2016 - 21:33

List Question

Show that series $a_{n+1} = \sqrt{1+\sqrt{a_n}}$ converges

Calculate radical expression without a calculator

Prove the inequality $\sqrt{a^2+b^2}+\sqrt{c^2+b^2}+\sqrt{a^2+c^2}<1+\frac{\sqrt2}{2}$

is $\sqrt[n]{n!}$ ever an integer?

When is a radical in its simplest form? Seemingly conflicting answers

How to find $x,y$ : $2^{x^2+y} + 2^{x + y^2} = 128$ , $\sqrt{x} + \sqrt{y} = 2\sqrt{2}$

Limit of $n -\sqrt{n^2+2n}$

Simplify $\sqrt{1+\sqrt 2}$

What is the sum of x+y?

Finding limit of sequence, done right: $a(n)=\sqrt{n^2+9}-\sqrt{n^2-n+9}$?

Prove $\sqrt{3} + \sqrt{5}$ is irrational

Convergence of a series with radicals: $\sum\limits_{n=1}^{\infty}\frac{\sqrt{n+2}-\sqrt{n+1}}{n}$

Please help me understand the steps to simplify this radical

I conjecture this inequality $\sqrt[4]{\frac{(xy+yz+xz)(x^2+y^2+z^2)}{9}}\ge\sqrt[3]{\frac{(x+y)(y+z)(z+x)}{8}}$

Please give me the method of writing $\sqrt{33 + 12 \sqrt 6}$ in the form $a + b \sqrt c$

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