若数列{an}满足a1=1,Sn+1=2an+Sn,(n∈N*)则前8项的和S8

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若数列{an}满足a1=1,Sn+1=2an+Sn,(n∈N*)则前8项的和S8若数列{an}满足a1=1,Sn+1=2an+Sn,(n∈N*)则前8项的和S8若数列{an}满足a1=1,Sn+1=2

若数列{an}满足a1=1,Sn+1=2an+Sn,(n∈N*)则前8项的和S8
若数列{an}满足a1=1,Sn+1=2an+Sn,(n∈N*)则前8项的和S8

若数列{an}满足a1=1,Sn+1=2an+Sn,(n∈N*)则前8项的和S8
S(n+1)=Sn+a(n+1)=2an+Sn
a(n+1)=2an
a(n+1)/an=2,为定值.
又a1=1,数列{an}是以1为首项,2为公比的等比数列.
S8=a1(q^8 -1)/(q-1)=1×(2^8 -1)/(2-1)=255