数列an满足a1>1,a(n+1)-1=an(an -1),且1/a1+1/a2+.1/a2012=2,a2013-4a1最小值为这是2012高三扬州期末调研的14题,求解

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数列an满足a1>1,a(n+1)-1=an(an -1),且1/a1+1/a2+.1/a2012=2,a2013-4a1最小值为这是2012高三扬州期末调研的14题,求解
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数列an满足a1>1,a(n+1)-1=an(an -1),且1/a1+1/a2+.1/a2012=2,a2013-4a1最小值为这是2012高三扬州期末调研的14题,求解
数列an满足a1>1,a(n+1)-1=an(an -1),且1/a1+1/a2+.1/a2012=2,a2013-4a1最小值为
这是2012高三扬州期末调研的14题,求解

数列an满足a1>1,a(n+1)-1=an(an -1),且1/a1+1/a2+.1/a2012=2,a2013-4a1最小值为这是2012高三扬州期末调研的14题,求解
a1>1,易知 ,对所有n ,an >1 , 等式两边取倒数,得1/( a (n+1)-1)=1/(an(an-1))=1/(an-1)-1/an
得,1/an=1/(an-1)-1/(a(n+1)-1) 则, 1/a1+1/a2+……1/a2012=1/a1-1/a2013=2
整理可得,a2013=(2-a1)/(3-2a1)
a2013-4a1=2(3-2a1)+1/(2(3-2a1))-11/2
≥2*√2(1-2a1)* 1/(2(1-2a1)) -11/2= -7/2
最小值是-7/2

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