问题 填空题
lim
n→∞
(
1
n2+1
+
2
n2+1
+
3
n2+1
+…+
2n
n2+1
)
=______.
答案

设A=

1
n2+1
+
2
n2+1
+
3
n2+1
+…+
2n
n2+1
=
1+2+3+…+2n
n2+1
=
2n2+n
n2+1

所以

lim
n→∞
(
1
n2+1
+
2
n2+1
+
3
n2+1
+…+
2n
n2+1
)=
lim
n→∞
A=
lim
n→∞
2n2+n
n2+1
=2

故答案为2.

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