已知数列{an}中,a1=3/5,数列an=2-1/an-1(n≥2,n∈N*）,数列{bn}满足bn=1/an-1

题目

已知数列{an}中,a1=3/5,数列an=2-1/an-1(n≥2,n∈N*）,数列{bn}满足bn=1/an-1
求证明数列{bn}是等差数列

答案

an=2-1/a(n-1)
an -1 = [a(n-1) - 1]/a(n-1)
1/(an -1) = a(n-1)/[a(n-1) - 1]
= 1+ 1/[a(n-1) - 1]
1/(an-1) - 1/[a(n-1) - 1] = 1
=> bn = 1/(an -1 ) 是等差数列