已知/XY-2/(这是绝对值的符号)与/Y-1/互为相反数.（1）求X,Y的值；（2）求1/(这是分数符号)XY+1/(X+1)(Y+1）+1/(X+2)(Y+2)+...+1/(X+2009)(Y+2009)的值.
问题描述：
已知/XY-2/(这是绝对值的符号)与/Y-1/互为相反数.
（1）求X,Y的值；
（2）求1/(这是分数符号)XY+1/(X+1)(Y+1）+1/(X+2)(Y+2)+...+1/(X+2009)(Y+2009)的值.
答
1:绝对值永远大于等于0|xy-2|+|y-1|=0|xy-2|=0 ,|y-1|=0xy=2y-1=0y=1,x=22:1/xy+1/(x+1)(y+1)+...+1/(x+2009)(y+2009)=1/2*1+1/3*2+1/4*3+...+1/2011*2010=1-1/2+1/2-1/3+1/3-1/4+...+1/2010-1/2011=1-1/2011=2010/2...