若|x-1|+|y-3|=0,求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+1/(x+6)(y+6）.+1/(x+2010)(y+2010)的值x=1,y=3,
问题描述：
若|x-1|+|y-3|=0,求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+1/(x+6)(y+6）.+1/(x+2010)(y+2010)的值
x=1,y=3,
答
|x-1|+|y-3|=0
|x-1|>=0,|y-3|>=0 -> x=1,y=3
1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+1/(x+6)(y+6）......+1/(x+2010)(y+2010)
=1/1*3+1/3*5+1/5*7+...+1/2011*2013
=1/2*(1/1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+...+1/2*(1/2011-1/2013) (裂项)
=1/2*(1-1/2013)
=1006/2013
答
有条件得 x=1,y=3
所以
原式=1/2（1/1-1/3+1/3-1/5+......-1/2011+1/2011-1/2013）
=1/2(1-1/2013)
=1006/2013
答
1006/2013