exec1.31.scm

(define (inc i) (+ i 1))

(define (product1 term a next b)
  (if (> a b)
    1
    (* (term a)
       (product1 term (next a) next b))))

(define (product2 term a next b)
  (define (iter a result)
    (if (> a b)
      result
      (iter (next a) (* (term a) result))))
  (iter a 1))

(define (pi/4 n)
  (define (nom k)
    (cond
      ((= 1 k) 2)
      ((even? k) (+ 2 k))
      (else (+ 1 k))))
  (define (denom k)
    (cond
      ((even? k) (+ 1 k))
      (else (+ 2 k))))
  (define (term k) (/ (nom k) (denom k)))
  (product2 term 1 inc n))

(define (pi n)
  (* 4.0 (pi/4 n)))
(pi 100000)