数列{an}和{bn}都是公差不为0的等差数列，且limn→∞anbn=3，则limn→∞a1+a2+…+annb2n=_．
问题描述：
数列{an}和{bn}都是公差不为0的等差数列，且
lim n→∞
=3，则an bn
lim n→∞
=______．
a1+a2+…+an
nb2n
答
设数列{an}和{bn}公差分别为d1，d2，
则
lim n→∞
=an bn
lim n→∞
=
a1 +(n−1)d1
b1 +(n−1)d 2
lim n→∞
=
+(1−a1 n
) d1
1 n
+(1−b1 n
)d 2
1 n
=3d1 d2
∴
lim n→∞
=
a1+a2+…+an
nb2n
lim n→∞
=na1 +
n(n−1)d1
2 n([b1 +(2n−1)d2]
=
d1
1 2 2d2
3 4
故答案为
．3 4