【摘要】 一般优选法资料中,都是用连分数理论,证明分数法数列:x₁=1/2, x_n=1/(1+x_n-1)（n=2,3,…） （1）的极限lim（x_n）=5^1/2-1/2=0.618033…≈0.618 （2）这是分数法和0.618法的关系。程汉晋为方便学习,给出了（2）的另一个证明。本文给出了四个简短的证明,这不仅有利于读者,还有利于优选法的改编。同时,（2）的证明,可作为大学一年级或中学数学课的例题。更多还原

【Abstract】 In the references of optimum seeking method, it is usually to prove the sequence of fraction methodhas the limitby the theory of continued fraction. This is the relation b tween the fraction method and the 0.618 method. For the convenience of applying and populariztion of optimum seeking method, Chen Han-jin(1) gave another proof of(2) in 1980.Four short proofs are given by the author in this paper. It is not only beneficial to the readers but also beheficial to reform optimum seeking method. Meanwhile, the proofs of(2) may be selected as the examples in teaching the limit of sequence for students in the first grade of universities or students of junior middle schools,更多还原