问题 选择题
设正数a,b满足
lim
x→2
(x2+ax-b)=4
,则
lim
n→∞
an+1+abn-1
an-1+2bn
=(  )
A.0B.
1
4
C.
1
2
D.1
答案

lim
x→2
(x2+ax-b)=4⇒4+2a-b=4⇒2a=b,

a
b
=
1
2

lim
n→∞
an+1+abn-1
an-1+2bn
=
lim
n→∞
a(
a
b
)
n
+
a
b
1
a
(
a
b
)
n
+2
=
lim
n→∞
a(
1
2
)
n
+
1
2
1
a
(
1
2
)
n
+2
=
1
4
.

故选B.

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