1.31 SICP (recursive)

product.scm

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

(define (inc x) (+ x 1))
(define (identity x) x)

(define (factorial n)
  (product identity 2 inc n))

(define (square x) (* x x))

(define (pi-approx n)
  (exact->inexact
   (* 4
     (/ (* 2 (product
	      (lambda (x)
		  (if (= x n) 
                    (* 2 x) 
                    (square (* 2 x)))) 
              2 inc n))
	   (product (lambda (x) (square (+ (* x 2) 1))) 1 inc (- n 1))))))