问题 选择题
已知
(x2-1)2+||xy|-2|
(x+1)(y+2)
=0
,则
1
xy
+
1
(x+1)(y+1)
+…+
1
(x+2001)(y+2001)
的值是(  )
A.
2000
2001
B.
2001
2002
C.
2002
2003
D.
2003
2004
答案

(x2-1)2+||xy|-2|
(x+1)(y+2)
=0,

∴x2-1=0,|xy|-2=0,x+1≠0,y+2≠0,

∴x=1,y=2,

∴原式=

1
1×2
+
1
2×3
+…+
1
2002×2003

=1-

1
2
+
1
2
-
1
3
+…+
1
2002
-
1
2003

=1-

1
2003

=

2002
2003

故选C.

单项选择题
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