已知两个等比数列{an},{bn}的前n项和分别为Sn,Tn,且满足SnTn=2n−13n−1,则a7b7=_.
问题描述:
已知两个等比数列{an},{bn}的前n项和分别为Sn,Tn,且满足
=Sn Tn
,则
2n−1
3n−1
=______. a7 b7
答
设两个等比数列的公比分别为q,q′,则
∵
=Sn Tn
,
2n−1
3n−1
∴
=
qn−1 q′n−1
,
2n−1
3n−1
∴q=2,q′=3,
∴
=a7 b7
×1 2
=q6 q′6
.32 729
故答案为:
.32 729