Question

已知等比数列{an}满足an＞0，n=1,2等，且a5*a(2n-5)=2的2n次方，则当n≥1时log2a1+log2a3+..+log2a(2n-1)=

Answer 1

a5 * a(2n-5) = 2^2n = a1 * a(2n-1) = a1a1q^(2n-2)
因为an > 0
所以:
a1q^(n-1) = an = 2^n
log2 an = n
原式 = 1 + 3 +....+ 2n-1
= n^2

Answer 2

a5 * a(2n-5) = 2^2n = a1 * a(2n-1) = a1a1q^(2n-2)
因为an > 0
所以:
a1q^(n-1) = an = 2^n
log2 an = n
原式 = 1 + 3 +....+ 2n-1
= n^2