题目内容
| 1 |
| 6 |
| 1 |
| 12 |
| 1 |
| 20 |
| 1 |
| 9900 |
考点：分数的巧算
专题：计算问题（巧算速算）
分析：
=
-
，
=
-
，
=
-
，…
=
-
，由此化简求解．
| 1 |
| 6 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 12 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 20 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 9900 |
| 1 |
| 99 |
| 1 |
| 100 |
解答：
解：
+
+
+…+
，
=（
-
）+（
-
）+（
-
）+…+（
-
），
=
-
+
-
+
-
+…+
-
，
=
-
，
=
．
| 1 |
| 6 |
| 1 |
| 12 |
| 1 |
| 20 |
| 1 |
| 9900 |
=（
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 99 |
| 1 |
| 100 |
=
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 99 |
| 1 |
| 100 |
=
| 1 |
| 2 |
| 1 |
| 100 |
=
| 49 |
| 100 |
点评：解决本题根据
-
=
（a为不是0的自然数）这一规律进行化简求解．
| 1 |
| a |
| 1 |
| a+1 |
| 1 |
| a(a+1) |
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