若｜x-1|+(xy-2)的平方＝０,求：1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……+1/(x+2006)(y+2006)的值

Question

若｜x-1|+(xy-2)的平方＝０,求：
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……+1/(x+2006)(y+2006)的值

Answer 1

由题意可知x=1,y=2,（因为要全都=0） 题目就变成1/(1*2)+1/(2*3).1/(2007*2008) 在拆分 变成1-1/2+1/2-1/3+1/3-1/4..1/2007-1/2008= 1-1/2008= 2007/2008