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=?
问题描述:
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=?
答
Sn=2An-1 ①S(n-1)=2A(n-1)-1 ②①-②得到:An=2An-2A(n-1)当n=1时,S1=2A1-1,即:A1=1An是首相为1,公比为2的等比数列An=2^(n-1)B(k+1)=2^(n-1)+BkB2-B1=1B3-B2=2..Bk-B(k-1)=2^(k-2)通加得到:Bk=2^(k-2)+3Tn=B1+B2+...