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a2.scm
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a2.scm
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"problem 1."
(define (factorial n) (if (= n 0)
1
(* n
(factorial (- n 1)))))
(define (n-choose-k n k) (if (or (< n k)
(< k 0))
0
(/ (factorial n)
(* (factorial (- n k))
(factorial k)))))
"problem 2."
(define (pow b e) (if (= e 0)
1
(* b
(pow b (- e 1)))))
"problem 3."
(define (zeno n) (if (= n 1)
(/ 1 2)
(+ (zeno (- n 1))
(/ 1 (pow 2 n)))))
"problem 4."
(define (num-digits n) (if (= (floor n) 0) 0 (+ (num-digits (/ n 10)) 1)))
"problem 5. (a)"
(define (a n) (pow 2 n))
"problem 5. (b)"
(define (num-ancestors n) (if (= n 1)
(a 1)
(+ (num-ancestors (- n 1))
(a n))))