Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Hatcher-Topology-of-Numbers · Problem 2.2.1
Continued Fractions
Mathematics — Algebraic Topology · infinite-continued-fractions-values
Problem Compute the values of the following infinite continued fractions:
(a) 1 4 ‾ \overline{\frac{1}{4}} 4 1 1 n ‾ \overline{\frac{1}{n}} n 1 n n n 1 2 + 1 3 ‾ \overline{\frac{1}{2} + \frac{1}{3}} 2 1 + 3 1 1 1 + 1 2 + 1 3 ‾ \frac{1}{1} + \overline{\frac{1}{2} + \frac{1}{3}} 1 1 + 2 1 + 3 1 1 1 + 1 2 + 1 1 + 1 6 ‾ \overline{\frac{1}{1} + \frac{1}{2} + \frac{1}{1} + \frac{1}{6}} 1 1 + 2 1 + 1 1 + 6 1 1 1 + 1 4 + 1 1 + 1 2 + 1 1 + 1 6 ‾ \frac{1}{1} + \frac{1}{4} + \overline{\frac{1}{1} + \frac{1}{2} + \frac{1}{1} + \frac{1}{6}} 1 1 + 4 1 + 1 1 + 2 1 + 1 1 + 6 1 1 2 + 1 3 + 1 5 ‾ \overline{\frac{1}{2} + \frac{1}{3} + \frac{1}{5}} 2 1 + 3 1 + 5 1 Browse the problem library