数学红对勾例2：若数列{an}满足a1=1,且an+1=an/(1+an),设数列{bn}的前n项和为Sn,且Sn=2-bn,n∈N﹡,

题目

数学红对勾例2：若数列{an}满足a1=1,且an+1=an/(1+an),设数列{bn}的前n项和为Sn,且Sn=2-bn,n∈N﹡,
求数列{bn/an}前n项和.
网上题目相同,但问的问题不同,请不要直接粘贴.

答案

a(n+1)=an/(1+an)1/a(n+1) = (1+an)/an = 1+1/an1/a(n+1) -1/an =11/an -1/a1=n-1an = 1/nSn=2-bnn=1, b1= 1bn = Sn -S(n-1) =-bn+b(n-1)bn = (1/2)b(n-1) = (1/2)^(n-1) .b1 =(1/2)^(n...