题目内容
计算：
+
+
+…+
=
．
| 1 |
| 2+4 |
| 1 |
| 2+4+6 |
| 1 |
| 2+4+6+8 |
| 1 |
| 2+4+…+20 |
| 9 |
| 22 |
| 9 |
| 22 |
分析：由原式可得=
+
+
+
+
+
+
+
+
，然后拆项为：
-
+（
-
）+（
-
）+…+（
-
），然后去括号解答即可．
| 1 |
| 6 |
| 1 |
| 12 |
| 1 |
| 20 |
| 1 |
| 30 |
| 1 |
| 42 |
| 1 |
| 56 |
| 1 |
| 72 |
| 1 |
| 90 |
| 1 |
| 110 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 10 |
| 1 |
| 11 |
解答：解：
+
+
+…+
，
=
+
+
+
+
+
+
+
+
，
=（
-
）+（
-
）+（
-
）+…+（
-
），
=
-
+
-
+
-
+…+
-
，
=
-
，
=
-
，
=
；
故答案为：
．
| 1 |
| 2+4 |
| 1 |
| 2+4+6 |
| 1 |
| 2+4+6+8 |
| 1 |
| 2+4+…+20 |
=
| 1 |
| 6 |
| 1 |
| 12 |
| 1 |
| 20 |
| 1 |
| 30 |
| 1 |
| 42 |
| 1 |
| 56 |
| 1 |
| 72 |
| 1 |
| 90 |
| 1 |
| 110 |
=（
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 10 |
| 1 |
| 11 |
=
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 10 |
| 1 |
| 11 |
=
| 1 |
| 2 |
| 1 |
| 11 |
=
| 11 |
| 22 |
| 2 |
| 22 |
=
| 9 |
| 22 |
故答案为：
| 9 |
| 22 |
点评：本题考查了常用的分数的拆分公式：
=
-
，应灵活掌握和应用．
| 1 |
| a(a+1) |
| 1 |
| a |
| 1 |
| a+1 |
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