Question

已知等比数列{an}满足an>0(n∈N*),且a5a2n-5=22n(n≥3),则当n≥1时,log2a1+log2a3+log2a5+…+log2a2n-1等于(　　)

(A)(n+1)2 (B)n2

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

 

Answer 1

【答案】

B

【解析】由等比数列的性质可知a5a2n-5=,

又a5a2n-5=22n,所以an=2n.

又log2a2n-1=log222n-1=2n-1,

所以log2a1+log2a3+log2a5+…+log2a2n-1=1+3+5+…+(2n-1)= =n2,故选B.