已知|ab+2|+|a+1|=0,求1/（a-1)(b+1)+1/(a-2)(b+2).+1/(a-2004)(b+2004)的值

题目

已知|ab+2|+|a+1|=0,求1/（a-1)(b+1)+1/(a-2)(b+2).+1/(a-2004)(b+2004)的值

答案

绝对值大于等于0,相加等于0,若有一个大于0,则另一个小于0,不成立
所以两个都等于0
所以ab+2=0,a+1=0
a=-1,ab=-2,b=-2/a=2
所以1/(a-1)(b+1)+1/(a-2)(b+2)+……+1/(a-2004)(b+2004)
=1/(-2)*3+(-3)*4+……+1/(-2005)*2006
=-(1/2*3+1/3*4+……+1/2005*2006)
=-[(1/2-1/3)+(1/3-1/4)+……+(1/2005-1/2006)
=-(1/2-1/2006)
=-501/1003