Question

若log2(9x)+log2(x-

1

3

)=1，则

lim

n→+∞

(1+x+x2+…xn)=______．

Answer 1

∵log2(9x)+log2(x-

1

3

)=1，
∴9x（x-

1

3

）=2，
解得x=-

1

3

（舍），或x=

2

3

．
∴

lim

n→+∞

(1+x+x2+…xn)
=

lim

n→+∞

1×(1-xn+1)

1-x

=

lim

n→+∞

1-( 2 3 )n+1

1- 2 3

=

1

1 3

=3．
故答案为3．