已知|ab+2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+...+1/(a+1999)(b+1999)的值

已知|ab+2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+...+1/(a+1999)(b+1999)的值
已知|ab+2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+...+1/(a+1999)(b+1999)的值

已知|ab+2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+...+1/(a+1999)(b+1999)的值
|ab-2|+|b-1|=0
ab-2=0
b-1=0
a=2,b=1
1/ab+1/(a+1)(b+1)+...+1/(a+1999)(b+1999)
=1/1•2+1/2•3+...+1/2000•2001
=1-1/2+1/2-1/3+1/3-1/4+...+1/2000-1/2001
=1-1/2001
=2000/2001