SICP 問題1.31

;; 再帰的プロセスでproduct
(define (product term a next b)
  (if (> a b)
      0
      (* (term a)
         (product term (next a) next b))))

;; 反復的プロセスでproduct
(define (product term a next b)
  (define (iter a result)
    (if (> a b)
        result
        (iter (next a) (* (term a) result))))
  (iter a 1))

(define (factorial n)
  (product identity 1 1+ n))

(define (pi-product n)
  (define (term i)
    (if (odd? i)
        (/ (+ i 1) (+ i 2))
        (/ (+ i 2) (+ i 1))))
    (product term 1 1+ n))

(define (pi n)
  (* 4 (pi-product n)))