题目内容
| 1 |
| 2×3 |
| 1 |
| 3×4 |
| 1 |
| 4×5 |
| 1 |
| 5×6 |
| 1 |
| 6×7 |
| 1 |
| 7×8 |
| 1 |
| 8×9 |
| 1 |
| 9×10 |
分析:此题可用分数拆项的方法解答.通过观察,每个分数的分子都是两个连续自然数的乘积,因此可以把每个分数拆成两个分数相减的形式,然后通过加减相互抵消,得出结果.
解答:解:
+
+
+
+
+
+
+
,
=
-
+
-
+
-
+
-
+
-
+
-
+
-
,
=
-
,
=
.
| 1 |
| 2×3 |
| 1 |
| 3×4 |
| 1 |
| 4×5 |
| 1 |
| 5×6 |
| 1 |
| 6×7 |
| 1 |
| 7×8 |
| 1 |
| 8×9 |
| 1 |
| 9×10 |
=
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 5 |
| 1 |
| 6 |
| 1 |
| 7 |
| 1 |
| 8 |
| 1 |
| 8 |
| 1 |
| 9 |
| 1 |
| 9 |
| 1 |
| 10 |
=
| 1 |
| 2 |
| 1 |
| 10 |
=
| 2 |
| 5 |
点评:此题中的分数属于两个连续自然数的乘积的形式,凡是这类型的分数,都可以把每个分数拆分成两个分数相减的形式.
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