参数取值范围问题
1/a(n+1)=1/2+1/(2an),1/a(n+1)-1=1/2*(1/an-1), ∵a1=2,∴1/a1-1=-1/2, ∴数列{1/an-1}是以-1/2为首项,1/2为公比的等比数列, ∴1/an-1=-1/2^n, ∴an=2^n/(2^n-1),an(an-1)=2^n/[(2^n-1)^2], a(n+1)[a(n+1)-1]:an(an-1)<1/2 ∑ai(ai-1)(i:1→n) =∑2^i/[(2^i-1)^2](i:1→n) <(2+4/9+8/49+16/225)*1/(1-1/16)<3, ∴整数m的最小值是3.
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