Euler's expansion

In 1737, the Swiss mathematician Leonhard Euler published a memoir De Fractionibus Continuis, which included a continued fraction expansion for e − 2 , where e is the base of the natural logarithms. In this fraction, the Ni are all 1 , and the Di are successively 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, ... Write a program that uses your cont-frac procedure from exercise 1.37 to approximate e , based on Euler's expansion.


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(check-equal? (round (* 1000000000000 (e 100))) 2718281828459.0) 
(check-equal? (round (* 100000 (e 10)))  271828.0)