(defn cont-frac [N D k]
  (defn iter [i]
    (cond
      (= k i) (/ (N i) (D i))
      (/ (N i) (+ (D i) (iter (+ i 1))))))
  (iter 1))

(defn cont-frac-iter [N D k]
  (defn iter [prev i]
    (if (>= i k)
      prev
      (cond
        (= i 1) (iter (/ (N (- k i)) (D (- k i))) (+ i 1))
        (iter (/ (N (- k i)) (+ (D (- k i)) prev)) (+ i 1)))))
  (iter 0 1))

(print (cont-frac (fn [i] 1.0)
                  (fn [i] 1.0)
                  12))

(print (cont-frac-iter (fn [i] 1.0)
                  (fn [i] 1.0)
                  12))