#lang sicp

(define (product term a next b)
  (define (iter a result)
    (if (> a b)
        result
        (iter (next a) (* result (term a)))))
  (iter a 1))

(define (pi-prod n)
  (define (pi-term i)
    (if (even? i)
        (/ (+ i 2) (+ i 1))
        (/ (+ i 1) (+ i 2))))
  (product pi-term 1 inc n))

;(define (inc x) (+ x 1))

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

(define (product-rec term a next b)
  (if (> a b)
      1
      (* (term a) (product-rec term (next a) next b))))