已知f(x)=3x/x+3数列{an}满足an=f(An-1)(n>1a不等于0已知f(x)=3x/x+3数列{an}满足an=f(An-1)(n>1a不等于0(1)求证{1/an}是AP等差数列(2)诺a1=1/4,求a40

Question

已知f(x)=3x/x+3数列{an}满足an=f(A n-1) (n>1 a不等于0
已知f(x)=3x/x+3数列{an}满足an=f(A n-1) (n>1 a不等于0
(1)求证{1/an}是AP等差数列
(2)诺a1=1/4,求a40

Answer 1

求什么,是{an}吗?
1.an=3(A n-1)/3+(A n-1),两边同取倒数,得：
1/an=3+(A n-1)/3(A n-1)=1/3+1/(A n-1),
所以,1/an-1/(A n-1)=1/3,即{1/an}是AP等差数列
2.由1可求