题目内容
先阅读，再解题：
因为1-
=
，
-
=
，
-
=
，…所以
+
+
+…+
=(1-
)+(
-
)+(
-
)+…+(
-
)=1-
+
-
+
-
+…+
-
=1-
．=
参照上述解法计算：
+
+
+…+
．
因为1-
| 1 |
| 2 |
| 1 |
| 1×2 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 2×3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 3×4 |
| 1 |
| 1×2 |
| 1 |
| 2×3 |
| 1 |
| 3×4 |
| 1 |
| 49×50 |
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 49 |
| 1 |
| 50 |
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 49 |
| 1 |
| 50 |
| 1 |
| 50 |
| 49 |
| 50 |
参照上述解法计算：
| 2013 |
| 1×3 |
| 2013 |
| 3×5 |
| 2013 |
| 5×7 |
| 2013 |
| 2011×2013 |
根据题意得：
原式=2013×
×（1-
+
-
+…+
-
）
=2013×
×
=1006．
原式=2013×
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 2011 |
| 1 |
| 2013 |
=2013×
| 1 |
| 2 |
| 2012 |
| 2013 |
=1006．
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