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)=
![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](/uploads/image/z/16009508-20-8.jpg?t=%E5%B7%B2%E7%9F%A5%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3an%EF%BC%9E0%2Cn%3D1%2C2%E7%AD%89%2C%E4%B8%94a5%2Aa%282n-5%29%3D2%E7%9A%842n%E6%AC%A1%E6%96%B9%2C%E5%88%99%E5%BD%93n%E2%89%A51%E6%97%B6log2a1%2Blog2)
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)
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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