(defn cont-frac [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))

(defn identity [i] 1.0)
(defn D [i]
  (let [n (+ i 1)]
   (cond
    (= (mod n 3) 0) (* (/ n 3) 2)
    1.0)))

(print (+ 2 (cont-frac identity D 100)))