已知数列{an}的前n项和Sn=n2(n∈N*),数列{bn}为等比数列,且满足b1=a1,2b3=b4 (1)求数列{an},{bn}的通项公式; (2)求数列{anbn}的前n项和.
问题描述:
已知数列{an}的前n项和Sn=n2(n∈N*),数列{bn}为等比数列,且满足b1=a1,2b3=b4
(1)求数列{an},{bn}的通项公式;
(2)求数列{anbn}的前n项和.
答
(1)由已知Sn=n2,得a1=S1=1当n≥2时,an=Sn-Sn-1=n2-(n-1)2=2n-1所以an=2n-1(n∈N*)由已知,b1=a1=1设等比数列{bn}的公比为q,由2b3=b4得2q2=q3,所以q=2所以bn=2n-1(2)设数列{anbn}的前n项和为Tn,则Tn=1×...