问题 填空题
若知|x1-1|+(x2-2)2+|x3-3|3+…+|x2011-2011|2011+(x2012-2012)2012=0
1
x1x2
+
1
x2x3
+
1
x3x4
+…+
1
x2011x2012
的值=______.
答案

根据题意得:x1-1=0,x2-2=0,x3-3=0,…x2011-2011=0,x2012-2012=0.

解得:x1=1,x2=2,x3=3,…,x2011=2011,x2012=2012.

1
x1x2
+
1
x2x3
+
1
x3x4
+…+
1
x2011x2012

=

1
x1
-
1
x2
+
1
x2
-
1
x3
+…+
1
x 2011
-
1
x2012

=

1
x1
-
1
x2012

=1-

1
2012

=

2011
2012

故答案是:

2011
2012

选择题
单项选择题