如果有理数x ,y满足|x-1|+(xy-2)² = 0 .(1)求x,y的值;(2)试求1/xy + 1/(x+1)(y+1) + 1/(x+2)(y+2) + .+ 1/(x+2009)(y+2009)的值 .楼下那位,就算不会那又怎么样啊,别这样鄙视人!

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如果有理数x ,y满足|x-1|+(xy-2)² = 0 .(1)求x,y的值;(2)试求1/xy + 1/(x+1)(y+1) + 1/(x+2)(y+2) + .+ 1/(x+2009)(y+2009)的值 .楼下那位,就算不会那又怎么样啊,别这样鄙视人!
如果有理数x ,y满足|x-1|+(xy-2)² = 0 .
(1)求x,y的值;
(2)试求1/xy + 1/(x+1)(y+1) + 1/(x+2)(y+2) + .+ 1/(x+2009)(y+2009)的值 .
楼下那位,就算不会那又怎么样啊,别这样鄙视人!

如果有理数x ,y满足|x-1|+(xy-2)² = 0 .(1)求x,y的值;(2)试求1/xy + 1/(x+1)(y+1) + 1/(x+2)(y+2) + .+ 1/(x+2009)(y+2009)的值 .楼下那位,就算不会那又怎么样啊,别这样鄙视人!
|x-1|+(xy-2)² = 0
则x-1=0 x=1
xy-2=0 y=2
1/xy + 1/(x+1)(y+1) + 1/(x+2)(y+2) + .+ 1/(x+2009)(y+2009)
=1/1x2 +1/2x3 +.+1/2010x2011
=1-1/2+1/2-1/3+...+1/2010-1/2011
=1-1/2011
=2010/2011

(1)|x-1|+(xy-2)² = 0
得x=1 xy=2 ∴ y=2
(2)1/1*2+1/2*3+1/3*4+...1/2010*2011
=1-1/2+1/2-1/3+1/3-1/4+1/2010-1/2011
=1-1/2011
=2010/2011