sum.scm

(define (sum-int a b)
  (if (> a b)
      0
      (+ a
         (sum-int (1+ a) b))))

(define (sum-sq a b)
  (if (> a b)
      0
      (+ (square a)
         (sum-sq (1+ a) b))))

(define (sum-pi a b)
  (if (> a b)
      0
      (+ (/ 1 (* a (+ a 2)))
         (sum-pi (+ a 4) b))))

;; Duplication!!
;; Abstract with procedure as first class citizen

(define (sum term a next b)
  (if (> a b)
      0
      (+ (term a)
         (sum term (next a) next b))))

(define (sum-int a b)
  (sum (lambda(i) i) a 1+ b))

(define (sum-sq a b)
 (sum square a 1+ b))

(define (sum-pi a b)
  (sum (lambda(i) (/ 1 (* i (+ i 4))))
       a
       (lambda(i) (+ i 4))
       b))