Solution to Exercise 1.30:

`(define (sum term a next b)`

(define (iter a result)

(if (> a b)

result

(iter (next a) (+ result (term a)))))

(iter a 0))

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# Month: May 2007

## Solution to SICP Exercise 1.30

## Solution to SICP Exercise 1.29

## The Luck Factor

## Solution to SICP Exercise 1.28

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Solution to Exercise 1.30:

`(define (sum term a next b)`

(define (iter a result)

(if (> a b)

result

(iter (next a) (+ result (term a)))))

(iter a 0))

Solution to Exercise 1.29:

`(define (sum term a next b)`

(if (> a b)

0

(+ (term a)

(sum term (next a) next b))))

```
```(define (inc n) (+ n 1))

`(define (simpsons-integral f a b n)`

(define (do-it h)

(define (y k)

(f (+ a (* k h))))

(define (simpson-term k)

(* (y k)

(cond ((or (= k 0) (= k n)) 1)

((odd? k) 4)

(else 2))))

(* (/ h 3) (sum simpson-term 0 inc n)))

(do-it (/ (- b a) n)))

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Solution to Exercise 1.28:

`(define (square x)`

(* x x))

```
```(define (expmod-with-trivial-sqrt-check base exp m)

(cond ((= exp 0) 1)

((even? exp)

(let* ((intermediate (expmod-with-trivial-sqrt-check base (/ exp 2) m))

(squared-mod (remainder (square intermediate) m)))

(if (and (not (or (= intermediate 1) (= intermediate (- m 1))))

(= squared-mod 1))

0

squared-mod)))

(else

(remainder (* base (expmod-with-trivial-sqrt-check base (- exp 1) m))

m))))

`(define (miller-rabin-test n)`

(define (try-it a )

(= (expmod-with-trivial-sqrt-check a (- n 1) n) 1))

(try-it (+ 1 (random (- n 1)))))