问题 填空题
设等差数列{an}的公差d是2,前n项的和为Sn,则
lim
n→∞
a2n
-n2
Sn
=______.
答案

由公差d=2,得到an=a1+2(n-1)=2n+a1-2,Sn=na1+

n(n-1)
2
×2=n2+n(a1-1)

lim
n→∞
a2n
-n2
Sn
=
lim
n→∞
3n2+4(a1-2)n+(a1-2)2
n2+n(a1-1)
=
lim
n→∞
3+
4(a1-2)
n
+
(a1-2)2
n2
1+
a1-1
n
=3

故答案为3.

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