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幼苗
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0=Delta = [2a(n+1)+a(n)+2]^2 - 4a(n+1)[2a(n)+4]
=[2a(n+1)+a(n)+2]^2 - 4*[2a(n+1)][a(n)+2]
=[2a(n+1)-a(n)-2]^2,
0=2a(n+1)-a(n)-2
a(n+1)=a(n)/2 + 1,
a(n+1)-2 = a(n)/2 - 1 = [a(n) - 2]/2
{a(n)-2}是首项为a(1)-2=-1,公比为1/2的等比数列.
a(n)-2 = -(1/2)^(n-1)
a(n) = 2 - 1/2^(n-1)
1年前
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