问题
选择题
已知等比数列{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 n2 D n2-1
答案
答案:C
由题知an=2n,log2a2n-1=2n-1,
∴log2a1+log2a3+…+log2a2n-1=1+3+…+(2n-1)=n2. 选C
已知等比数列{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 n2 D n2-1
答案:C
由题知an=2n,log2a2n-1=2n-1,
∴log2a1+log2a3+…+log2a2n-1=1+3+…+(2n-1)=n2. 选C