List questions from continued-fractions

Published on 07 Mar 2017 - 20:33

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Length of continued fraction

Published on 09 Mar 2017 - 10:17

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Weird large K symbol

Published on 09 Mar 2017 - 22:05

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Show $f(x)=1-\frac{1}{x\left(\lvert x\rvert_2\right)}$ converges on $0$ in finite steps

Published on 10 Mar 2017 - 9:07

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Is there a name for the reciprocal of the fractional part of a number?

Published on 25 Mar 2026 - 18:59

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How to show every rational number can be expressed as two different continued fractions?

Published on 27 Mar 2017 - 11:53

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Solution for continued fraction

Published on 27 Mar 2017 - 18:12

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Is the sequence defined by $a_{n+1} = \frac{1}{a_n} + 1$ convergent?

Published on 27 Mar 2017 - 20:24

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Prove $q_n \alpha - p_n = \frac{(-1)^n}{\alpha_{n+1}q_n +q_{n-1}}$

Published on 28 Mar 2017 - 8:09

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If $\alpha \in (0,1)$ is an irrational number, show that $\alpha = \sum_{n=0}^{\infty} \frac{(-1)^n}{q_{n+1}q_{n}}$

Published on 29 Mar 2017 - 10:13

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A continued fraction with a delayed repeating part

Published on 31 Mar 2017 - 18:33

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Continued fraction of $\sqrt{67} - 4$

Published on 03 Apr 2017 - 12:54

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Can anything interesting be said about this fake proof?

Published on 26 Mar 2026 - 8:04

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Do you know of any instance when a continued fraction is really of use?

Published on 08 Apr 2017 - 5:24

109

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Denominators in Convergents of Continued Fraction

Published on 08 Apr 2017 - 19:08

List Question

Solve the equation $x=[2;2,2,\ldots,2,2,x]$

Length of continued fraction

Weird large K symbol

Show $f(x)=1-\frac{1}{x\left(\lvert x\rvert_2\right)}$ converges on $0$ in finite steps

Is there a name for the reciprocal of the fractional part of a number?

How to show every rational number can be expressed as two different continued fractions?

Solution for continued fraction

Is the sequence defined by $a_{n+1} = \frac{1}{a_n} + 1$ convergent?

Prove $q_n \alpha - p_n = \frac{(-1)^n}{\alpha_{n+1}q_n +q_{n-1}}$

If $\alpha \in (0,1)$ is an irrational number, show that $\alpha = \sum_{n=0}^{\infty} \frac{(-1)^n}{q_{n+1}q_{n}}$

A continued fraction with a delayed repeating part

Continued fraction of $\sqrt{67} - 4$

Can anything interesting be said about this fake proof?

Do you know of any instance when a continued fraction is really of use?

Denominators in Convergents of Continued Fraction

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