inf

(defun inf_fact (n)
  (let ((pcur 2))
    (loop (setq pcur (+ 2 (/ 3.0 pcur))) (setq n (1- n))
      (when (= n 0) (return pcur))))
  )
INF_FACT

(inf_fact 1)
3.5
(inf_fact 2)
2.857143
(inf_fact 10)
2.999977
(inf_fact 11)
3.000008
(inf_fact 12)
2.999998
(inf_fact 13)
3.000001
(inf_fact 14)
3.0
(inf_fact 15)
3.0