Question

Closed form solution for $\sum_{n=1}^\infty\frac{1}{1+\frac{n^2}{1+\frac{1}{\stackrel{\ddots}{1+\frac{1}{1+n^2}}}}}$.

score 1k · Answer 1 · 2026-03-25 09:21:30

1k

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Closed form solution for $\sum_{n=1}^\infty\frac{1}{1+\frac{n^2}{1+\frac{1}{\stackrel{\ddots}{1+\frac{1}{1+n^2}}}}}$.

Published on 25 Mar 2026 - 9:21

score 354 · Answer 2 · 2015-01-12 02:22:01

354

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score 121 · Answer 3 · 2015-01-16 17:02:10

121

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How is Lagrange's $2\sqrt{D}$ bound on partial denominators proven for periodic regular continued fractions of quadratic irrationals

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score 119 · Answer 4 · 2015-01-28 17:32:43

119

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score 53 · Answer 5 · 2026-03-26 14:34:52

53

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score 123 · Answer 6 · 2015-02-02 10:12:55

123

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score 679 · Answer 7 · 2026-03-26 13:46:36

679

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score 1.8k · Answer 8 · 2015-02-08 18:10:56

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score 197 · Answer 9 · 2015-02-18 19:28:46

197

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score 65 · Answer 10 · 2015-02-19 21:25:26

65

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score 139 · Answer 11 · 2026-03-27 16:47:41

139

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score 296 · Answer 12 · 2015-03-01 19:51:01

296

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score 45 · Answer 13 · 2015-03-02 22:40:51

45

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score 389 · Answer 14 · 2015-03-03 19:05:15

389

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Published on 03 Mar 2015 - 19:05

score 250 · Answer 15 · 2015-03-03 21:44:26

250

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Published on 03 Mar 2015 - 21:44

List Question

Closed form solution for $\sum_{n=1}^\infty\frac{1}{1+\frac{n^2}{1+\frac{1}{\stackrel{\ddots}{1+\frac{1}{1+n^2}}}}}$.

Continued fraction of $e^{-2\pi n}$

How is Lagrange's $2\sqrt{D}$ bound on partial denominators proven for periodic regular continued fractions of quadratic irrationals

Continued fraction approximation

Coefficients of the polynomials generated by $f_0=x,\ f_{i+1}=f_i\pm\dfrac1{f_i}$.

Good rational approximations using continued fractions?

Closest rational approximation of $\sqrt x$ with denominator having prime powers $\lt n$

Good and best rational approximations

Continued Fraction, Closest Neighbours

On the asymptotics of a continued fraction

Is there any elegant formalization of fractional numbers?

Simple Finite Continued Fraction

Continued Fraction summation representation

Why are there no continued fraction representation for $\pi$ obeying mathematical rules?

Integral of a Continued Fraction

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