题目内容
计算：
+
+
+…+
．
| 2009 |
| 2×4 |
| 2009 |
| 4×6 |
| 2009 |
| 6×8 |
| 2009 |
| 4016×4018 |
考点：分数的简便计算
专题：运算定律及简算
分析：先提取2009，然后再根据分数拆项的方法，把算式进行相互抵消，从而化简得解．
解答：
解：
+
+
+…+
=2009×（
+
+
+…+
）
=2009×
×（
-
+
-
+
-
+…+
-
）
=
×（
-
）
=
×
-
×
=
-
=
=502．
| 2009 |
| 2×4 |
| 2009 |
| 4×6 |
| 2009 |
| 6×8 |
| 2009 |
| 4016×4018 |
=2009×（
| 1 |
| 2×4 |
| 1 |
| 4×6 |
| 1 |
| 6×8 |
| 1 |
| 4016×4018 |
=2009×
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 6 |
| 1 |
| 6 |
| 1 |
| 8 |
| 1 |
| 4016 |
| 1 |
| 4018 |
=
| 2009 |
| 2 |
| 1 |
| 2 |
| 1 |
| 4018 |
=
| 2009 |
| 2 |
| 1 |
| 2 |
| 2009 |
| 2 |
| 1 |
| 4018 |
=
| 2009 |
| 4 |
| 1 |
| 4 |
=
| 2008 |
| 4 |
=502．
点评：本题的关键是正确的进行分数拆项．
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