问题 填空题
已知数列{an}满足a1=1,an+an+1=(
1
3
)
n
(n∈N*)
,Sn=a1+3•a2+32•a3+…+3n-1•an,则4Sn-3nan=______.
答案

由Sn=a1+3•a2+32•a3+…+3n-1•an

所以3Sn=3a1+32•a2+33•a3+…+3n•an

相加4Sn=a1+3(a1+a2)+…+3n-1•(an-1+an)+3n•an

所以4Sn-3nan=1+3(

1
3
)1+32(
1
3
)
2
+…+3n-1(
1
3
)
n-1
=n.

故答案为n.

判断题
判断题