> 数学 >
已知{an}是公差不为零的等差数列,如果sn是{an}的前n项的和,那么
lim
n→∞
nan
sn
等于______.
人气:294 ℃ 时间:2020-06-22 22:49:27
解答
设an=a1+(n-1)d,sn=na1+
n(n−1)
2
d,代入得
lim
n→∞
nan
sn
=
lim
n→∞
na1+n(n−1)d
na1+
n(n−1)
2
d
=
lim
n→∞
a1
n−1
+d
a1
n−1
+
d
2
=2
故答案为2
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