#lang racket

(define (k-con n f init)
  (let loop([i n] [r 0])
    (cond [(= 1 i) (+ init r)]
          [else (loop (sub1 i) (/ 1 (+ r (f i))))])))
          
;; ith convergent of sqrt(2)
(define (sqrt2 i)
  (k-con i (λ (x) 2) 1))

;; ith convergent of e
(define (con-e i)
  (k-con i (λ (x) 
             (let-values ([(q r) (quotient/remainder x 3)])
               (if (zero? r) (* 2 q) 1)))
         2))

(numerator (con-e 100))

• 相关文章
• 全局相关文章