已知数列{an}满足a1=4/3,2-a(n+1)=12/an+6
问题描述：
已知数列{an}满足a1=4/3,2-a(n+1)=12/an+6
则1/a1+2/a2+.1/an=?
答
2-a(n+1)=12/(an+6)a(n+1) = 2an/(an+6)1/a(n+1) = (an+6)/[2an]1/a(n+1) + 1/4 = 3(1/an + 1/4)[1/a(n+1) + 1/4] / (1/an + 1/4) = 3(1/an + 1/4)/ (1/a1+1/4) = 3^(n-1)(1/an + 1/4) = 3^(n-1)1/an = 3^(n-1) -1/4...