∵y=(n 2+n)x 2-(2n+1)x+1=(nx-1)[(n+1)x-1],
∴由y=0得x=
1
n 或x=
1
n+1
∴A n(
1
n+1 ,0),B n(
1
n ,0),
∴|A nB n|=
1
n -
1
n+1
∴|A 1B 1|+|A 2B 2|+…+|A 1992B 1992|=(1-
1
2 )+…+(
1
1992 -
1
1993 )=1-
1
1993 =
1992
1993
故选B.
∵y=(n 2+n)x 2-(2n+1)x+1=(nx-1)[(n+1)x-1],
∴由y=0得x=
1
n 或x=
1
n+1
∴A n(
1
n+1 ,0),B n(
1
n ,0),
∴|A nB n|=
1
n -
1
n+1
∴|A 1B 1|+|A 2B 2|+…+|A 1992B 1992|=(1-
1
2 )+…+(
1
1992 -
1
1993 )=1-
1
1993 =
1992
1993
故选B.