sicp 1.37 1.38

;; p1.37
(define cont-frac
  (lambda (fn fd k)
    (define frac-inside
      (lambda (x)
        (if (= x k)
            (/ (fn x) (fd x))
            (/ (fn x) (+ (fd x) (frac-inside (+ x 1)))))))
    (frac-inside 1)))
;; b
(define cont-frac-i
  (lambda (fn fd k)
    (define frac-i
      (lambda (init k)
        (if (= k 1)
            (/ (fn 1) (+ (fd 1) init))
            (frac-i (/ (fn k) (+ (fd k) init)) (- k 1)))))
    (frac-i 0 k)))


;; p1.38
(define get-e
  (lambda (k)
    (+ 2 (cont-frac-i (lambda (x) 1.0)
           (lambda (x)
             (cond
               [(= (remainder x 3) 2) (* 2 (+ 1 (quotient x 3)))]
               [else 1]))
           k))))