<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, We give a generalization the resut of Roger B. Nelsen, by giving a closed form expression for x =<inline-formula><alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_AMNS.2019.1.00006_eq_002.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>[</mo> <mrow><msub><mi>a</mi><mn>0</mn></msub><mo>,</mo><msub><mi>a</mi><mn>1</mn></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mi>a</mi><mi>k</mi></msub><mo>,</mo><mover accent="true"><mrow><msub><mi>b</mi><mn>1</mn></msub><mo>,</mo><mo>⋯</mo><msub><mi>b</mi><mi>m</mi></msub></mrow><mo stretchy="true">¯</mo></mover></mrow> <mo>]</mo></mrow><mo>,</mo></mrow></math>
<tex-math>$\left[ {{a}_{0}},{{a}_{1}},\cdots ,{{a}_{k}},\overline{{{b}_{1}},\cdots {{b}_{m}}} \right],$</tex-math></alternatives></inline-formula></p></abstract>

In this paper, We give a generalization the resut of Roger B. Nelsen, by giving a closed form expression for x =

[ a0,a1,⋯,ak,b1,⋯bm¯ ],
$\left[ {{a}_{0}},{{a}_{1}},\cdots ,{{a}_{k}},\overline{{{b}_{1}},\cdots {{b}_{m}}} \right],$

Proof without words: Periodic continued fractions

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Proof without words: Periodic continued fractions"}

In this paper, We give a generalization the resut of Roger B. Nelsen, by giving a closed form expression for x =

[ a0,a1,⋯,ak,b1,⋯bm¯ ],
$\left[...

Proof without words: Periodic continued fractions

Published Online: Apr 26, 2019

Page range: 57 - 60

Received: Feb 06, 2019

Accepted: Mar 22, 2019

DOI: https://doi.org/10.2478/AMNS.2019.1.00006

Keywords
Continued fractions, periodic, proof without words

© 2019 Amara Chandoul, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Proof without words: Periodic continued fractions

Published Online: Apr 26, 2019

Page range: 57 - 60

Received: Feb 06, 2019

Accepted: Mar 22, 2019

DOI: https://doi.org/10.2478/AMNS.2019.1.00006

KeywordsContinued fractions, periodic, proof without words

© 2019 Amara Chandoul, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Continued fractions, periodic, proof without words