Fibonacci Numbers and Continued Fractions

Abstract

In this chapter we will be mostly concerned with expressions of the form

$$ {q_0} + {\frac{1}{{{q_1} + \frac{1}{{{q_2} + }}}}_{ \ddots + \frac{1}{{qn}}}} $$

(3.1)

where q ₁, q ₂,…,q _n are positive integers, and q ₀ is a nonnegative integer. Thus, in contrast to q ₁, q ₂,…,q _n , the number q ₀ may be equal to zero. In what follows we will always assume that q ₀ has this somewhat special status, without mentioning it on each occasion.