Question

若

lim

n→∞

(a+1)n+1

n+2

=2（a∈R），则

lim

x→1

ax2-3x+2

x-a

=______．

Answer 1

∵

lim

n→∞

(a+1)n+1

n+2

=2=

lim

n→∞

 

a+1+ 1 n

1+ 2 n

=a+1，∴a=1．
则

lim

x→1

ax2-3x+2

x-a

=

lim

n→∞

 

(x-1)(x-2)

x-1

=

lim

n→∞

（x-2）=

lim

n→∞

 （-1）=-1，
故答案为-1．