已知数列{An}满足:A1=0An+1=An+2n则A2011的值为?
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已知数列{An}满足:A1=0An+1=An+2n则A2011的值为?
已知数列{An}满足:A1=0An+1=An+2n则A2011的值为?
已知数列{An}满足:A1=0An+1=An+2n则A2011的值为?
∵An+1-An=2n
∴An-An-1=2(n-1)
∴An=A1+(A2-A1)+(A3-A2)+…+(An-An-1)
=0+2×1+2×2+2×3+…2(n-1)
=2×[1+2+3+…+(n-1)]
=2×[1+(n-1)]×(n-1)/2
=n(n-1)
∴A2011=2011×2010=4042110
an-a(n-1)=2n-2
a(n-1)-a(n-2)=2n-4……
a2-a1=2 叠加 an-a1=2+4+……+2n-2=n(n-1) an=n(n-1)
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