Exercise 5.26: Use the monitored stack to
explore the tail-recursive property of the evaluator (5.4.2).
Start the evaluator and define the iterative factorial procedure from
1.2.1:


(define (factorial n)
  (define (iter product counter)
    (if (> counter n)
        product
        (iter (* counter product)
              (+ counter 1))))
  (iter 1 1))

Run the procedure with some small values of 
  n
.  Record the maximum stack
depth and the number of pushes required to compute 
  
    n
    !
  
 for each of these
values.


 You will find that the maximum depth required to evaluate 
  
    n
    !
  
 is independent
of 
  n
.  What is that depth?

 Determine from your data a formula in terms of 
  n
 for the total number of
push operations used in evaluating 
  
    n
    !
  
 for any 
  
    n
    ≥
    1
  
.  Note that the
number of operations used is a linear function of 
  n
 and is thus determined
by two constants.