Category: Tail Recursion

Continued Fraction Tail Recursive

An infinite continued fraction is an expression of the form

The infinite continued fraction expansion with the Ni and the Di all equal to 1 produces 1/, where is the golden ratio.
One way to approximate an infinite continued fraction is to truncate the expansion after a given number of terms. Such a truncation — a so-called k-term finite continued fraction — has the form

Suppose that n and d are procedures of one argument (the term index i) that return the Ni and Di of the terms of the continued fraction.

Define a procedure cont-frac such that evaluating (cont-frac n d k) computes the value of the k-term finite continued fraction. Check your procedure by approximating 1/ using

(cont-frac (lambda (i) 1.0)
(lambda (i) 1.0)
k)

for successive values of k.