(1)a1=1,a(n+1)=1/2an+1,(2)a1=1,a(n+1)=1/3an-2/3求an,Sn
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(1)a1=1,a(n+1)=1/2an+1,(2)a1=1,a(n+1)=1/3an-2/3求an,Sn
(1)a1=1,a(n+1)=1/2an+1,(2)a1=1,a(n+1)=1/3an-2/3
求an,Sn
(1)a1=1,a(n+1)=1/2an+1,(2)a1=1,a(n+1)=1/3an-2/3求an,Sn
(1)a(n+1)=1/2an+1
设a(n+1)-m=1/2(an-m)
a(n+1)=1/2an+1/2m
∴m=2
∴a(n+1)-2=1/2(an-2)
∴﹛an-2﹜是等比数列
∴an-2=(a1-2)(1/2)^(n-1)=-(1/2)^(n-1)
∴an=2-(1/2)^(n-1)
Sn=2n-1×(1-1/2^n)/(1-1/2)=2n-2(1-1/2^n)
(2)a(n+1)=1/3an-2/3
设a(n+1)-m=1/3(an-m)
a(n+1)=1/3an+2/3m
∴m=-1
∴a(n+1)+1=1/3(an+1)
∴﹛an+1﹜是等比数列
∴an+1=(a1+1)(1/3)^(n-1)=2×(1/3)^(n-1)
∴an=2×(1/3)^(n-1)-1
Sn=2×(1-1/3^n)/(1-1/3)-n
=3(1-1/3^n)-n
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