题目内容
若知|x1-1|+(x2-2)2+|x3-3|3+…+|x2011-2011|2011+(x2012-2012)2012=0，
则
+
+
+…+
的值=______．
则
| 1 |
| x1x2 |
| 1 |
| x2x3 |
| 1 |
| x3x4 |
| 1 |
| x2011x2012 |
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．
则
+
+
+…+
=
-
+
-
+…+
-
=
-
=1-
=
．
故答案是：
．
解得：x1=1，x2=2，x3=3，…，x2011=2011，x2012=2012．
则
| 1 |
| x1x2 |
| 1 |
| x2x3 |
| 1 |
| x3x4 |
| 1 |
| x2011x2012 |
=
| 1 |
| x1 |
| 1 |
| x2 |
| 1 |
| x2 |
| 1 |
| x3 |
| 1 | ||
|
| 1 |
| x2012 |
=
| 1 |
| x1 |
| 1 |
| x2012 |
=1-
| 1 |
| 2012 |
=
| 2011 |
| 2012 |
故答案是：
| 2011 |
| 2012 |
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