已知数列{an}满足a1=1,an+a（n+1）=（1/3）的n次方（n∈N）,Sn=a1+3a2+3²a3……+3n-1次方an

由Sn=a1+3a2+3²a3……+3n-1次方an 得
3Sn= 3a1+3²a2……+3n-1次方an-1+3n次方×an
相加4Sn=a1+3(a1+a2)+……3n-1次方*(an-1+an)+3n次方an=a1+(n-1)+3n次方×an
故：4Sn-3的n次方×an=a1+n-1=n