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2.(上海卷)設(shè)數(shù)列的前項和為,且對任意正整數(shù),。(1)求數(shù)列的通項公式?(2)設(shè)數(shù)列的前項和為,對數(shù)列,從第幾項起?
.解(1) ∵an+ Sn=4096, ∴a1+ S1=4096, a1 =2048.
當n≥2時, an= Sn-Sn-1=(4096-an)-(4096-an-1)= an-1-an ∴= an=2048()n-1.
(2) ∵log2an=log2[2048()n-1]=12-n, ∴Tn=(-n2+23n).
由Tn<-509,解得n>,而n是正整數(shù),于是,n≥46. ∴從第46項起Tn<-509.