《中学生数学》2003年12月上期高一课外练习中,有这样一题:已知函数f(x)=-2x+2,x∈[0.5,1],设f(x)的反函数为y=g(x),a1=1,a2=g(a1),…,an=g(an-1),求数列{an)的通项公式. 由于g(x)=1-1/2x,此题实质上就是:已知a1=1,an=1-1/2a-1,求an. 我在解答这一题时,是依次求出{an}的前 In the “High School Mathematics for Middle School Students” in the previous high school exercise in December 2003, there was such a question: the known function f(x)=-2x+2, x∈[0.5,1], and the inverse function of f(x) is y=g(x),a1=1,a2=g(a1),...,an=g(an-1), find the general term formula of the series {an). Since g(x)=1-1/2x , This question is essentially: Known a1=1, an=1-1/2a-1, find an. When I answer this question, it is to find {an} before