Question

How to calculate $x_{n}= \sqrt{n+ \sqrt{n- 1+ \sqrt{n- 2+ \sqrt{\cdots + \sqrt{2+ \sqrt{1}}}}}}$ without using surd signs

score 240 · Answer 1 · 2020-12-27 09:59:54

240

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How to calculate $x_{n}= \sqrt{n+ \sqrt{n- 1+ \sqrt{n- 2+ \sqrt{\cdots + \sqrt{2+ \sqrt{1}}}}}}$ without using surd signs

Published on 27 Dec 2020 - 9:59

score 46 · Answer 2 · 2021-01-01 17:13:56

46

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why the sequence $ \{q_n \} $ converges to $ + \infty $?

Published on 01 Jan 2021 - 17:13

score 105 · Answer 3 · 2021-01-01 17:17:22

105

Views

Evaluating $2+\cfrac{1}{2+\cfrac{1}{2+\cdots}}$. Why can we say $2+\frac1x=x$?

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score 87 · Answer 4 · 2026-03-27 10:12:55

87

Views

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score 106 · Answer 5 · 2021-01-05 10:40:38

106

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score 82 · Answer 6 · 2021-01-07 01:42:27

82

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score 75 · Answer 7 · 2021-01-07 06:38:10

75

Views

Evaluate $360 (\frac{1}{15}+\frac{1}{105}+\frac{1}{315}+⋯).$

Published on 07 Jan 2021 - 6:38

score 38 · Answer 8 · 2021-01-17 14:58:58

38

Views

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score 309 · Answer 9 · 2021-01-26 12:40:13

309

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score 166 · Answer 10 · 2026-03-26 22:13:12

166

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score 245 · Answer 11 · 2026-03-29 14:19:59

245

Views

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score 113 · Answer 12 · 2021-02-05 11:36:21

113

Views

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Published on 05 Feb 2021 - 11:36

score 383 · Answer 13 · 2026-03-27 11:45:13

383

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score 892 · Answer 14 · 2021-02-08 05:13:22

892

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Is there a general way to convert a continued fraction into a recursive formula?

Published on 08 Feb 2021 - 5:13

score 77 · Answer 15 · 2026-02-23 04:20:09

77

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Analytic Continuation of Fractions

Published on 23 Feb 2026 - 4:20

List Question

How to calculate $x_{n}= \sqrt{n+ \sqrt{n- 1+ \sqrt{n- 2+ \sqrt{\cdots + \sqrt{2+ \sqrt{1}}}}}}$ without using surd signs

why the sequence $ \{q_n \} $ converges to $ + \infty $?

Evaluating $2+\cfrac{1}{2+\cfrac{1}{2+\cdots}}$. Why can we say $2+\frac1x=x$?

the second order continued fraction expansion of an irrational number and the distance to its closest integer

Approximation: Understanding a property of continued fractions and convergents

Integral part of an infinite simple continued fraction

Evaluate $360 (\frac{1}{15}+\frac{1}{105}+\frac{1}{315}+⋯).$

Solving equation involving finite continued fraction

Rationality of negative continued fractions

Negative continued fraction of Euler Mascheroni constant

Irrationality of ${\pi}$ and $e^{x/y}$

continuous fraction for $ 30/\pi^2 $

355/113 and small odd cubes

Is there a general way to convert a continued fraction into a recursive formula?

Analytic Continuation of Fractions

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