求(2)题一二小题
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求(2)题一二小题
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![求(2)题一二小题](/uploads/image/z/19892280-48-0.jpg?t=%E6%B1%82%282%29%E9%A2%98%E4%B8%80%E4%BA%8C%E5%B0%8F%E9%A2%98%26nbsp%3B)
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(1)用数学归纳法.
A(n+1)=An^2-nAn+1=An(An-n)+1>=An*2+1>=(n+2)*2+1=2n+5>n+1+2
(2)因为an>=n+2,所以an-n>=2
A(n+1)=An(An-n)+1>=2An+1
A(n+1)+1>=2(An+1)
1/(A(n+1)+1)<=1/(An+1)*1/2
1/(1+a1)=1/4,1/(1+a2)<=1/2*1/4
1/(1+a1) + 1/(1+a2) + ……+1/(1+an) <=1/4(1+1/2+1/4+.+1/2^(n-1))<1/4*2=1/2
当且仅当n=1时取等号.