题目内容
计算：
+
+
+
+
+
+
+
=
| 1 |
| 3 |
| 2 |
| 5 |
| 5 |
| 7 |
| 7 |
| 8 |
| 9 |
| 20 |
| 10 |
| 21 |
| 11 |
| 24 |
| 12 |
| 35 |
3
| 9 |
| 20 |
3
．| 9 |
| 20 |
分析：通过观察，前4个分数运用拆分，把后4个分数进行拆分．每个分数拆成两个分数的和，然后运用加法结合律简算．
解答：解：
+
+
+
+
+
+
+
=
+
+
+
+（
+
）+（
+
）+（
+
）+（
+
）
=（
+
+
）+
+（
+
+
）+（
+
）+（
+
+
）
=1+
+1+1+
=3+（
+
）
=3+
=3
．
故答案为：3
．
| 1 |
| 3 |
| 2 |
| 5 |
| 5 |
| 7 |
| 7 |
| 8 |
| 9 |
| 20 |
| 10 |
| 21 |
| 11 |
| 24 |
| 12 |
| 35 |
=
| 1 |
| 3 |
| 2 |
| 5 |
| 5 |
| 7 |
| 7 |
| 8 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 3 |
| 1 |
| 7 |
| 1 |
| 3 |
| 1 |
| 8 |
| 1 |
| 5 |
| 1 |
| 7 |
=（
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 5 |
| 7 |
| 1 |
| 7 |
| 1 |
| 7 |
| 7 |
| 8 |
| 1 |
| 8 |
| 2 |
| 5 |
| 1 |
| 5 |
| 1 |
| 5 |
=1+
| 1 |
| 4 |
| 4 |
| 5 |
=3+（
| 1 |
| 4 |
| 1 |
| 5 |
=3+
| 9 |
| 20 |
=3
| 9 |
| 20 |
故答案为：3
| 9 |
| 20 |
点评：先进行分数裂项，然后运用加法结合律，求出结果．
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