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题目
题型:卢湾区一模难度:来源:
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.
核心考点
试题【limn→∞(1n2+1+2n2+1+3n2+1+…+2nn2+1)=______.】;主要考察你对函数极值与最值等知识点的理解。[详细]
举一反三
已知直线l与曲线y=x2+3x-1切于点(1,3),则直线l的斜率为(  )
A.-1B.1C.3D.5
题型:花都区模拟难度:| 查看答案
lim
x→1
(
2x+1
x2+x-2
-
1
x-1
)
=______.
题型:陕西难度:| 查看答案
lim
n→∞
(
1
2
+
1
4
+…+
1
2n
)
=______.
题型:不详难度:| 查看答案
lim
x→1
x2-6x+5
x2-1
=a
,则a=______,
lim
n→∞
(
1
a
+
1
a2
+
1
a3
+…+
1
an
)
=______.
题型:石景山区一模难度:| 查看答案
lim
x→1
x2-1
2x2-x-1
=(  )
A.0B.1C.
1
2
D.
2
3
题型:四川难度:| 查看答案
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