I am reading SICP and read this recitation. I use MIT/GNU Scheme as MIT course 6.5151 (6.905) does with version 12.1.

I am stuck at Problem 3. I tried to use . So I have code

(define (e x)
  (newline)
  (display (/ 1.0 x))
  (newline)
  (display (+ 1.0 (/ 1.0 x)))
  (newline)
  (display x)
  (expt (+ 1.0 (/ 1.0 x)) x))
(e (expt 10 100))

It has answer 1.. Here I use display to check where the resolution is not as expected. It turns out (display (+ 1.0 (/ 1.0 x))) outputs 1. which is unexpected.

The instructor solution uses Taylor series which is different from the above idea.