# Tagged Questions

A is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number.

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### How to write continued fraction as polynomial?

I have \begin{align} r(x)= 1 + \frac{x}{\frac{1}{2}+\frac{x-1}{-1+\frac{x+1}{1+\frac{x-1}{-1}}}} \end{align} for an interpolation problem, and I need to write $r(x)$ such that nominator and ...
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### Evaluating $\frac{2}{3-\frac{2}{3-\frac{2}{3-\ldots} } }$

What is the value of the fraction $\frac{2}{3-\frac{2}{3-\frac{2}{3-\ldots} } }$? I let $x=\frac{2}{3-\frac{2}{3-\frac{2}{3-\ldots} } }$ and hence $x=\frac{2}{3-x}$ which gives $x=1$ or $x=2$. ...
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### functions on a continued fraction expansion

Let $x$ be an irrational number with continued fraction expansion $[a_0;a_1,a_2,\ldots]$. Is there an $x$ and a non-identity function $f$ such that $f(x)=[f(a_0);f(a_1),f(a_2),\ldots]$. Given that I ...
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### Cube root of two continued fraction

I know there is a nice way of getting the continued fraction expansion of quadratic irrationals mainly because they recur after a point, and if they recur after a point they are quadratic irrationals. ...
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### Question in fraction (not simple )

I have a question and its answer but I don't know how can i solve $$\frac {37}{13} = 2+ \frac {1}{x+\frac{1}{5+\frac{1}{y}}}$$ the answer $x =1, y=2$ Could any one explain how to solve this ?? ...
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### How to find value of $x+y+z+u+v+w$

let $x,y,z,u,v,w$ be positive integer numbers,and such $$1949(xyzuvw+xyzu+xyzw+xyvw+xuvw+zuvw+xy+xu+xw+zu+zw+vw+1)=2004(yzvw+yzu+yzw+uvw+y+u+w)$$ Find this value of $$x+y+z+u+v+w=?$$ My try: maybe ...
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### Definition of $1 + \cfrac{1}{2+\cfrac{1}{3+\cfrac{1}{4+\cfrac{1}{\ddots}}}}$

Is there a definition of $1 + \cfrac{1}{2+\cfrac{1}{3+\cfrac{1}{4+\cfrac{1}{\ddots}}}}$? I am somewhat familiar with continued fractions; that is, I am aware that their convergence depends on whether ...