Question

数学题。。谁帮我做一下啊？？！

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，至少比你好啊。你会做啊，那就说啊。别这样鄙视人！

Answer 1

|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

Answer 2

(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