若a1=3,an+1=3an+3^n+1 1)设bn=an/3^n 证明:数列{bn}是等比数列 (2)求数列{an}的

(1)a(n+1)=3an+3^(n+1)a(n+1)/3^(n+1)-an/3^n= 1{an/3^n} 是等差数列,d=1an/3^n-a1/3^1=n-1an/3^n= nan = n。3^n(2)bn = an/3^n = n{bn}是等差数列letS = 1。3^1+2。3^2+。。。+n。3^n (1)3S = 1。3^2+2。3^3+。。。+n。3^(n+1) (2)(2)-(1)2S = n。3^(n+1)-(3+3^2+。。。+3^n)=n。3^(n+1)- (3/2)(3^n-1)S = 3 + (6n-3)。3^nSn = a1+a2+。。。+an = S = 3 + (6n-3)。3^n