数列an满足an+1=2an-1且a1=3,bn=an-1/anan+1,数列bn前n项和为Sn.求数列an通项an,

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数列an满足an+1=2an-1且a1=3,bn=an-1/anan+1,数列bn前n项和为Sn.求数列an通项an,数列an满足an+1=2an-1且a1=3,bn=an-1/anan+1,数列bn

数列an满足an+1=2an-1且a1=3,bn=an-1/anan+1,数列bn前n项和为Sn.求数列an通项an,
数列an满足an+1=2an-1且a1=3,bn=an-1/anan+1,数列bn前n项和为Sn.求数列an通项an,

数列an满足an+1=2an-1且a1=3,bn=an-1/anan+1,数列bn前n项和为Sn.求数列an通项an,
a(n+1)=2an-1
a(n+1)-1=2(an-1)
[a(n+1)-1]/(an-1)=2,为定值.
a1-1=3-1=2
数列{an}是以2为首项,2为公比的等比数列.
an=2×2^(n-1)=2^n
数列{an}的通项公式为an=2^n
bn=a^(n-1)/[ana(n+1)]=2^(n-1)/[2^n×2^(n+1)]=1/2^(n+2)=(1/8)(1/2)^(n-1)
数列{bn}是以1/8为首项,1/2为公比的等比数列.
Sn=(1/8)(1-1/2^n)/(1-1/2)=(1/4)(1-1/2^n)

an+1=2an-1
a(n+1)-1=2(an-1) 数列{an-1} 是等比数列首项a1-1=2 公比q=2
an-1=2*2^(n-1)=2^n
an=[2^n]+1

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