Question

数列满足a1=3,a(n)乘a(n-1)=2a(n-1)-1,求证{1/a(n)-1}为等差数列 括号里为下标

Answer 1

a1=3,a2=5/3,a3=4/5.

and,1/(a1-1)=1/2,

1/(a2-1)=3/2,

1/(a3-1)=5/2,

so,假设为1等差数列.

1/[a(n)-1]-1/[a(n-1)-1]=1,so,本式子为常数是1的等差数列