设数列{an}的前n项和为Sn,数列{Sn}的前n项和为Tn,满足Tn=2Sn-n2,n∈N*.(1)求a1的...
问题详情:设数列{an}的前n项和为Sn,数列{Sn}的前n项和为Tn,满足Tn=2Sn-n2,n∈N*.(1)求a1的值;(2)求{an}的通项公式.【回答】解:(1)当n=1时,T1=2S1-1,而T1=S1=a1,所以a1=2a1-1,解得a1=1.(2)n≥2时,Sn=Tn-Tn-1=2Sn-n2-[2Sn-1-(n-1)2]=2Sn-2Sn-1-2n+1.所以Sn=2...