谁说回答问题就一定要收钱的,呵呵
解,
|ab-2|与|b-1|互为相反数
|ab-2|+|b-1|=0
|ab-2|,|b-1|都为非负数,两者和为0.两者必定都为0
ab-2=0,b-1=0
a=2,b=1
所以
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+1999)(b+1999)
=1/2*1+1/3*2+1/4*3+.+1/2001*2000
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2000-1/2001)
=1-1/2001
=2000/2001