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+log2

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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)=

A5*A（2n-5）=2^(2n)(n≥3)
A1*Q^4 * A1*Q^(2n-6)=2^(2n)
A1^2*Q^(2n-2)=2^(2n)
An=2^n
所以log2（A1）+log2（A3）+……+log2[A（2n-1）]=1+2+3+……+(2n-1)=[(2n-1)*(1+2n-1)]/2=n*(2n-1)

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