1
vote
1answer
109 views

find the value of 1/(2+1/(4+1/(4+1/(…))))

the question is to find the value of this ugly non-stopping fraction $$\frac{1}{2+\frac{1}{4+\frac{1}{4+\frac{1}{\ldots}}}}$$. I have totally no clue; thanks for the help! How am I suppose to solve ...
1
vote
1answer
103 views

Continued fractions with $n$ layers

Solve the equation $$x=2+\dfrac1{2+\dfrac1{...2+\dfrac1{2+\dfrac1x}}}$$ Where there are n layers in the fraction
15
votes
1answer
1k views

What was Ramanujan's solution?

The wikipedia entry on Ramanujan contains the following passage: One of his remarkable capabilities was the rapid solution for problems. He was sharing a room with P. C. Mahalanobis who had a ...
7
votes
4answers
488 views

How to detect when continued fractions period terminates

I'm doing continued fractions arithmetic. Is there a method to detect when a continued fractions period terminates? Let me give you an example: $\sqrt{2} = [1; \overline{2}]$, $\sqrt{7} = [2; ...
1
vote
1answer
2k views

Converting a square root into a simple continued fraction

One can convert a square root $\sqrt{n}$ into a continued fraction $[a_0; \overline{a_1, a_2, \dots , a_k}]$ following the algebraic algorithm explained here: ...
1
vote
3answers
191 views

Continued fraction form for rational numbers less than $1$

How could we convert a rational number (less than $1$) to the continued fraction form? This is probably an extension of this question. After reading Bill Dubuque's answer here and here, I got ...