等差数列{an},等比数列{bn}各项都是正数,a1=b1,a(2n+1)右下标=b(2n+1)右下标.则有a(n+1)
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a(n+1)=[a1+a(2n+1)]/2=[b1+b(2n+1)]/2≥√[b1*b(2n+1)]=b(n+1)
(这里应用了等差中项和等比数列中项的性质以及平均值不等式)
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