已知等比數列{an}滿足an>0,n=1,2,…,且a5•a2n-5=22n(n≥3),則當n≥1時,log2a1+log2a3+…+log2a2n-1=() A.(n-1)2B. n2C.(n+1)2D. n2-1

已知等比數列{an}滿足an>0,n=1,2,…,且a5•a2n-5=22n(n≥3),則當n≥1時,log2a1+log2a3+…+log2a2n-1=() A.(n-1)2B. n2C.(n+1)2D. n2-1

∵a5•a2n-5=22n=an2,an>0,∴an=2n,∴log2a1+log2a3+…+log2a2n-1=log2(a1a3…a2n-1)=log221+3+…+(2n-1)=log22n2=n2.故選B.