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已知数列an满足1/(2+an+1)-1/(2+an)=2,a1=-3/2,则a8=
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已知数列an满足1/(2+an+1)-1/(2+an)=2,a1=-3/2,则a8=
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∵1/(2+an+1)-1/(2+an)=2
∴数列{1/(2+an)｝是等差数列,公差d=2
1/(2+an)=1/(2+a1)+(n-1)d
=1/(2-3/2)+(n-1)*2
=2+2n-2
=2n
2+an=1/2n
an=1/2n-2
a8=1/2*8-2
=1/16-2
=31/16
∴数列{1/(2+an)｝是等差数列,公差d=2
1/(2+an)=1/(2+a1)+(n-1)d
=1/(2-3/2)+(n-1)*2
=2+2n-2
=2n
2+an=1/2n
an=1/2n-2
a8=1/2*8-2
=1/16-2
=31/16
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