已知{an}为等差数列,Sn为其前n项喝,且2Sn=an+2n²(1)求an.Sn
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已知{an}为等差数列,Sn为其前n项喝,且2Sn=an+2n²(1)求an.Sn
2a(1)=2s(1)=a(1)+2,a(1)=s(1)=2,
2s(n)=a(n)+2n^2,
2s(n+1)=a(n+1)+2(n+1)^2,
2a(n+1)=2s(n+1)-2s(n)=a(n+1)-a(n) + 2(2n+1),
a(n+1) = - a(n) + 4n + 2,
a(n+1) - 2(n+1) = -a(n) + 2n = -[a(n)-2n],
{a(n)-2n}是首项为a(1)-2=0,公比为(-1)的等比数列.
a(n)-2n = 0*(-1)^(n-1) = 0,
a(n) = 2n,
2s(n) = a(n) + 2n^2 = 2n + 2n^2 = 2n(n+1),
s(n) = n(n+1).
2s(n)=a(n)+2n^2,
2s(n+1)=a(n+1)+2(n+1)^2,
2a(n+1)=2s(n+1)-2s(n)=a(n+1)-a(n) + 2(2n+1),
a(n+1) = - a(n) + 4n + 2,
a(n+1) - 2(n+1) = -a(n) + 2n = -[a(n)-2n],
{a(n)-2n}是首项为a(1)-2=0,公比为(-1)的等比数列.
a(n)-2n = 0*(-1)^(n-1) = 0,
a(n) = 2n,
2s(n) = a(n) + 2n^2 = 2n + 2n^2 = 2n(n+1),
s(n) = n(n+1).
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