#
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.

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