等比数列{an}的首项为a1=a,公比q≠1,则1a1a2+1a2a3+…+1anan+1=q2n?1a2q(q2n?q2n?2)q2n?1a2q(q2n?q2n?2

2025-05-14 09:33:19
推荐回答(1个)
回答(1):

1
a1a2
1
a2a3
,…,
1
anan+1
是首项为
1
a1a2
=
1
a2q
,公比为
1
q2

1
a1a2
+
1
a2a3
+…+
1
anan+1
=
1
a2q
(1? (
1
q2
)
n
1?
1
q2
=
q2n?1
a2q(q2n?q2n?2)

故答案为:
q2n?1
a2q(q2n?q2n?2)