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a(n+1)=an^2+4an+2
a(n+1)+2=(an+2)^2
两边取lg对数得
lg[a(n+1)+2]=lg(an+2)^2
lg[a(n+1)+2]=2lg(an+2)
lg[a(n+1)+2]/lg(an+2)=2
所以,{lg(an+2)}是等比数列
2)lg(an+2)=lg(a1+2)*[2^(n-1)]=2^(n+10lg2=lg2^(2^(n+1)
an+2=2^[2^(n+1)]
an=2^[2^(n+1)]-2
bn=1/2[1/(an+1)+1/(an+3)]=1/2{1/[2^(2^n+1)]-1]+1/1/[2^(2^n+1)]+1]
=
a(n+1)+2=(an+2)^2
两边取lg对数得
lg[a(n+1)+2]=lg(an+2)^2
lg[a(n+1)+2]=2lg(an+2)
lg[a(n+1)+2]/lg(an+2)=2
所以,{lg(an+2)}是等比数列
2)lg(an+2)=lg(a1+2)*[2^(n-1)]=2^(n+10lg2=lg2^(2^(n+1)
an+2=2^[2^(n+1)]
an=2^[2^(n+1)]-2
bn=1/2[1/(an+1)+1/(an+3)]=1/2{1/[2^(2^n+1)]-1]+1/1/[2^(2^n+1)]+1]
=
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