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(2n-1)
B.(n+1)2
C.n2
D.(n-1)2
答案
答案:C
log2a1+log2a3+…+log2a2n-1=log2(a1a3…a2n-1)=log2(a5·a2n-5)=n2.
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(2n-1)
B.(n+1)2
C.n2
D.(n-1)2
答案:C
log2a1+log2a3+…+log2a2n-1=log2(a1a3…a2n-1)=log2(a5·a2n-5)=n2.