Exercise 1.38 · 习题

Exercise 1.38: 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 N

i are all 1, and

the D

i 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.

练习 1.38：1737 年，瑞士数学家莱昂哈德·欧拉发表了论文《De Fractionibus Continuis》，其中给出了 e − 2 的连分式展开，其中 e 是自然对数的底数。在这个分式中，所有 Nᵢ 均为 1，Dᵢ 依次为 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, …。编写一个程序，利用练习 1.37 中的 cont-frac 过程，基于欧拉展开近似计算 e 的值。