作业帮已知等比数列an满足an大于0,n=1,2.且a5乘a2n-5=2的2n(n大于等于3）已知等比数列｛an}满足an>0,n=1,2,且a5-a2n-5=2^2n(n>=3),则当n>=1时，log2a1+log2a3+…log2a2n-1=
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已知等比数列an满足an大于0,n=1,2.且a5乘a2n-5=2的2n(n大于等于3）已知等比数列｛an}满足an>0,n=1,2,且a5-a2n-5=2^2n(n>=3),则当n>=1时，log2a1+log2a3+…log2a2n-1=
已知等比数列an满足an大于0,n=1,2.且a5乘a2n-5=2的2n(n大于等于3）
已知等比数列｛an}满足an>0,n=1,2,且a5-a2n-5=2^2n(n>=3),则当n>=1时，log2a1+log2a3+…log2a2n-1=
已知等比数列an满足an大于0,n=1,2.且a5乘a2n-5=2的2n(n大于等于3）已知等比数列｛an}满足an>0,n=1,2,且a5-a2n-5=2^2n(n>=3),则当n>=1时，log2a1+log2a3+…log2a2n-1=
∵a[n]是等比数列.又有a[5]*a[2n-5]=2^2n ∴a[1]*a[2n-1]=2^2n
设a[n]得公比为q.∵a[1]*q^n-1=a[n],a[2n-1]=a[1]*q^2n-2,
∴a[1]*a[2n-1]=(a[1]*q*n-1)²=a[n]² ∴a[n]²=2^2n 从而 a[n]=2^n
∵log2 a[1]+log2 a[2]+…+log2a[2n-1]=log2(a[1]*a[2]*…a[2n-1])
=log2[(a[1]*a[2n-1])*(a[2]*a[2n-2])…
=log2[2^n²]
=n^2
a5=a1*d^4
a2n-1=a1*d^2n-4
*
a1^d^a2n=2^2n
a1*d^n=2^n
an+1=2^n
an=2^n-1
∵a5•a2n-5=22n=a，an＞0，
∴an=2n，
∴log2a1+log2a3+…+log2a2n-1=log2（a1a3a2n-1）=log221+3++（2n-1）=log22n2=n2．
∵a5•a2n-5=22n=a，an＞0，
∴an=2n，
∴log2a1+log2a3++log2a2n-1=log2（a1a3a2n-1）=log221+3++（2n-1）=log22n2=n2．