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设{an}是各项互不相等的正数等差数列,{bn}是各项互不相等的正数等比数列,a1=b1,a2n+1=b2n+1,则(  )
A. an+1>bn+1
B. an+1≥bn+1
C. an+1<bn+1
D. an+1=bn+1
人气:400 ℃ 时间:2020-08-31 19:59:34
解答
因为等差数列{an}和等比数列{bn}各项都是正数,且a1=b1,a2n+1=b2n+1
所以an+1-bn+1=
a1+a2n+1
2
-
b1b2n+1
=
a1+a2n+1−2
a1+a2n+1
2
=
(
a1
a2n+1
)2
2
≥0.
即 an+1≥bn+1
故选 A.
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