若|x-1|+|y-2|=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2009)(y+2009)的值十分钟内的答案,经过认可,

由已知可得：x=1,y=2
原式=1/2+1/6+1/12+1/20+……+1/n(n+1)
因为1/n(n+1)=1/n-1/(n+1)
所以原式=1-1/2 +1/2-1/3 +1/3-1/4+ ……+1/2010-1/2011
=1-1/2011=2010/2011

因为|x-1|+|y-2|=0,所以X=1，Y=2
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+......+1/(x+2009)(y+2009)
=1/2+1/(X+1)-1/(Y+1))+1/(x+2)-1/(Y+2)+···+1/(x+2009)-1/(y+2009)
=1/2+1/2-1/3+1/3-1/4+···+1/3000-1/3001
=1-1/3001
=3000/3001

由题知，
若|x-1|+|y-2|=0,
则
|x-1|=0且|y-2|=0,
所以，
x=1且y=2
所以，
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+......+1/(x+2009)(y+2009)
=1/(1*2)+1/(2*3)+1/(3*4)+......+1/(2010*2011)
=(2-1)/(1*2)+(3-2)/(2*3)+(4-3)/(3*4)+......+(2011-2010)/(2010*2011)
=[1/1-1/2]+[1/2-1/3]+[1/3-1/4]+......+[1/2010-1/2011]
=1-1/2011
=2010/2011
希望您采纳~~~

x=1，y=2
原式=1/（1*2）+1/（2*3）+。。。+1/（2010*2011）
=1-1/2+1/2-1/3+。。。+1/2010-1/2011
=1-1/2011
=2010/2011

|x-1|+|y-2|=0
x=1 y=2
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+......+1/(x+2009)(y+2009)
=1/1x2+1/2x3+1/3x4+........+1/2010x2011
=1-1/2+1/2-1/3+1/3-1/4+......+1/2010-1/2011
=1-1/2011
=2010/2011

|x-1|+|y-2|=0 |x-1|>=0 |y-2|>=0
x=1,y=2
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+......+1/(x+2009)(y+2009)
=1/xy+1/2*1/3+1/3*1/4+1/4*1/5+1/5*1/6+...+1/2008*1/2009+1/2009*1/3000+1/3000*1/3001
=1/2+[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/2008-1/2009)+(1/2009-1/3000)+(1/3000-1/3001)]
=1/2+1/2-1/3001=3000/3001

|x-1|+|y-2|=0，x=1，y=2
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+......+1/(x+2009)(y+2009）=1/2+1/2*/13+1/3*1/3+1/4*1/5.。。。。1/3000*1/3001
1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.。。。+1/3000-1/3001
=1-1/3001=3000/3001

|x-1|+|y-2|=0
x=1,y=2
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2009)(y+2009)
=1/2+1/6+1/12+.+1/(2010*2011)
=1-1/2+1/2-1/3+.+1/2010-1/2011
=1-1/2011
=2010/2011

x=1,y=2
1/(x+n)(y+n)=[1/(x+n)-1/(y+n)]/(y-x)=1/(n+1)-1/(n+2)
原式＝1-1/2011=2010/2011

x=1，y=2
原式=1/（1*2）+1/（2*3）+......+1/（2010*2011）
=1-1/2+1/2-1/3+.......+1/2010-1/2011
=1-1/2011
=2010/2011