（1）3an=2Sn+n ...①
3an+1=2Sn+1 +n+1 ...②
②-①得：3an+1 -3an=2an+1 +1
即an+1=3an +1 ==＞an+1 +1/2=3(an+1/2)
an+1 +1/2 / an+1/2=3
∵S1=a1 ∴当n=1时代入①得 a1=1
即得证 数列{an+1/2}为等比数列,首相a1为1,公比q为3
（2）T1=S1=1
Tn=S1+S2+S3+.+Sn ...③
Tn+1=S1+S2+S3+.+Sn+Sn+1 ...④
④-③得 Tn+1 -Tn=Sn+1=3^(n+1）/2 -1/2 (3的n+1次方)
∴Tn=（Tn- Tn-1）+(Tn-1 -Tn-2)+.(T2-T1)+T1
=[-3+3*（3^n -1）/2]/2-(n-1)*(1/2)+1
=[3^(n+1)-2n-4]/4