Question

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．0

B． 1 4

C． 1 2

D．1

Answer 1

∵

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．