若数列an满足a1=1,an+1(+1下标)=1/2an + 1(1/2an与+1分开),求an

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若数列an满足a1=1,an+1(+1下标)=1/2an + 1(1/2an与+1分开),求an
若数列an满足a1=1,an+1(+1下标)=1/2an + 1(1/2an与+1分开),求an

若数列an满足a1=1,an+1(+1下标)=1/2an + 1(1/2an与+1分开),求an
a(n+1)=an/2 + 1
∴a(n+1)-2=(an-2)/2
∴设bn=an-2,则b(n+1)=bn/2
即bn是等比数列,公比1/2,首项b1=a1-2=-1
∴bn=-(1/2)^(n-1)
∴an=bn+2=2-(1/2)^(n-1)