Infinite Continued Fraction - iterative and recursive
Your solutions look good.  

I don't see any significantly different way to do the recursive solution.  My preferences for whitespace (mostly concerning the if) are a little different.  Also, I wouldn't define a function for next in this situation.  If for some reason you don't want to simply put (+ n 1) as an argument a let expression would be more applicable.

(define (cont-frac n_i d_i k)
   (define (recurse n)
     (if (= n k) 
         (/ (n_i k) (d_i k)) 
         (/ (n_i n) (+ (d_i n) (recurse (+ n 1)))) ))
   (recurse 1))


OR

(define (cont-frac n_i d_i k)
   (define (recurse n)
     (if (= n k) 
         (/ (n_i k) (d_i k)) 
         (let ((next_n (+ n 1)))
           (/ (n_i n) (+ (d_i n) (recurse next_n)))) ))
   (recurse 1))


PS - write a function for the nth_odd_square and try this

(/ 4.0 (+ 1 (i-cont-frac nth_odd_square (lambda (i) 2.0) 500000)))