Some hopefully not-too-cryptic hints for problem 1.31.

Approach #1

1. Consider writing:

(define (pi/4 terms)
  (/ (numer terms) (denom terms)))

and then write numer and denom. in terms of product and expt.

2. (expt 2 terms) is your friend.

3. Treat one term as two numbers in the numerator and two numbers in the denominator.

(numer 1) --> 2 * 4
(numer 2) --> 2 * 4 * 4 * 6

(denom 1) --> 3 * 3
(denom 2) --> 3 * 3 * 5 * 5

Etc.

Approach #2

Write a function pi-term that takes an integer input and returns a fraction you can multiply by other pi-terms.

(pi-term 1) --> 2/3
(pi-term 2) --> 4/3
(pi-term 3) --> 4/5
(pi-term 4) --> 6/5
(pi-term 5) --> 6/7

Etc.