若limx→1x2-6x+5x2-1=a,则a=______,limn→∞(1a+1a2+1a3+…+1an)=______.

若limx→1x2-6x+5x2-1=a,则a=______,limn→∞(1a+1a2+1a3+…+1an)=______.

题型:石景山区一模难度:来源:
lim
x→1
x2-6x+5
x2-1
=a
,则a=______,
lim
n→∞
(
1
a
+
1
a2
+
1
a3
+…+
1
an
)
=______.
答案
lim
x→1
x2-6x+5
x2-1
=
lim
x→1
(x-1)(x-5)
(x+1)(x-1)
=
lim
x→1
x-5
x+1
=-2,
∴由
lim
x→1
x2-6x+5
x2-1
=a
,知a=-2.
lim
n→∞
(
1
a
+
1
a2
+
1
a3
+…+
1
an
)
=
lim
n→∞
1
-2
[1-(-
1
2
)
n
]
1- (-
1
2
=-
1
3

答案:-2,-
1
3
举一反三
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
lim
n→+∞
n2+2n+1
2n2-n+1
=______.
题型:奉贤区一模难度:| 查看答案
lim
x→1
x-1
x2+3x-4
=______.
题型:湖南难度:| 查看答案
lim
n→∞
[1-(
b
1-b
)
n
]=1
,则b的取值范围是(  )
A.
1
2
<b<1
B.-
1
2
<b<
1
2
C.b<
1
2
D.0<b<
1
2
题型:湖南难度:| 查看答案
计算:
lim
n→∞
2n-1
3n+1
=______.
题型:嘉定区一模难度:| 查看答案
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