等差数列{an}的各项均为正数,a1=3,前n项和为Sn,{bn}为等比数列,b1=1,且b2S2=64,b3S3=960求an和bn

题目

等差数列{an}的各项均为正数,a1=3,前n项和为Sn,{bn}为等比数列,b1=1,且b2S2=64,b3S3=960求an和bn
求和：1/S1+1/S2+……+1/Sn

答案

设{an}公差为d,数列各项均为正,则d≥0；设{bn}公比为q.b2S2=64 b3S3=960(b1q)×(2a1+d)=64 (b1q²)×(3a1+3d)=960a1=3 b1=1代入,整理,得q(d+6)=64 (1)q²(d+3)=320 (2)(1)²/(2)(d+6)²/(d+3)=64/5...