Topology of Numbers · Problem 2.2.1

Continued Fractions — Allen Hatcher

Mathematics — Number Theory · infinite-continued-fractions-values

Problem

Compute the values of the following infinite continued fractions: (a)

\overline{\frac{1}{4}}

(b)

\overline{\frac{1}{n}}

for an arbitrary positive integer

n

(c)

\overline{\frac{1}{2} + \frac{1}{3}}

and

\frac{1}{1} + \overline{\frac{1}{2} + \frac{1}{3}}

(d)

\overline{\frac{1}{1} + \frac{1}{2} + \frac{1}{1} + \frac{1}{6}}

and

\frac{1}{1} + \frac{1}{4} + \overline{\frac{1}{1} + \frac{1}{2} + \frac{1}{1} + \frac{1}{6}}

(e)

\overline{\frac{1}{2} + \frac{1}{3} + \frac{1}{5}}