设数列{An}的前n项和满足Sn=2An-1(1不是下标)(n=1,2,3,...),数列{Bn}满足B1=3,B(k+1)=Ak+Bk(k+1为下标)(k=1,2,3,...),则数列{Bn}的前n项和Tn=?

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设数列{An}的前n项和满足Sn=2An-1(1不是下标)(n=1,2,3,...),数列{Bn}满足B1=3,B(k+1)=Ak+Bk(k+1为下标)(k=1,2,3,...),则数列{Bn}的前n项和Tn=?
设数列{An}的前n项和满足Sn=2An-1(1不是下标)(n=1,2,3,...),数列{Bn}满足B1=3,B(k+1)=Ak+Bk(k+1为下标)(k=1,2,3,...),则数列{Bn}的前n项和Tn=?

设数列{An}的前n项和满足Sn=2An-1(1不是下标)(n=1,2,3,...),数列{Bn}满足B1=3,B(k+1)=Ak+Bk(k+1为下标)(k=1,2,3,...),则数列{Bn}的前n项和Tn=?
Sn=2An-1 ①
S(n-1)=2A(n-1)-1 ②
①-②得到:An=2An-2A(n-1)
当n=1时,S1=2A1-1,即:A1=1
An是首相为1,公比为2的等比数列
An=2^(n-1)
B(k+1)=2^(n-1)+Bk
B2-B1=1
B3-B2=2
.
.
Bk-B(k-1)=2^(k-2)
通加得到:Bk=2^(k-2)+3
Tn=B1+B2+B3+…Bn
=3n+1/4+1/3+1+4+…2^(n-2)
=3n+1/4[1-(1/2)^(n+2)]/1/2
=3n+1/2[1-(1/2)^(n+2)]
嘿嘿

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