题目内容


等比数列{an}满足an>0,n=1,2,….且a5·a2n-5=22n(n≥3),则当n≥1时,log2a1+log2a3+…+log2a2n-1=(  )

A.(n-1)2                              B.(n+1)2 

C.n(2n-1)                             D.n2


 D

[解析] ∵等比数列{an}满足an>0,a5·a2n-5=22n(n≥3),∴a5·a2n-5=(an)2=22n,∴an=2n.∴log2a1+log2a3+…+log2a2n-1=log2(a1a3·…·a2n-1)=log2(an)n=log2(2n)n=log22n2n2.


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