题目内容
1-
-
-
-
-
-
=
.
| 2 |
| 3 |
| 2 |
| 9 |
| 2 |
| 27 |
| 2 |
| 81 |
| 2 |
| 243 |
| 2 |
| 729 |
| 1 |
| 729 |
| 1 |
| 729 |
分析:通过观察,先把从1里连续减去这几个分数,等于从1里减去它们的和,再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-
-
-
-
-
-
,
=1-(
+
+
+
+
+
),
=1-(1-
+
-
+
-
+
-
+
-
+
-
),
=1-(1-
),
=1-1+
,
=
| 2 |
| 3 |
| 2 |
| 9 |
| 2 |
| 27 |
| 2 |
| 81 |
| 2 |
| 243 |
| 2 |
| 729 |
=1-(
| 2 |
| 3 |
| 2 |
| 9 |
| 2 |
| 27 |
| 2 |
| 81 |
| 2 |
| 243 |
| 2 |
| 729 |
=1-(1-
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 9 |
| 1 |
| 9 |
| 1 |
| 27 |
| 1 |
| 27 |
| 1 |
| 81 |
| 1 |
| 81 |
| 1 |
| 243 |
| 1 |
| 243 |
| 1 |
| 729 |
=1-(1-
| 1 |
| 729 |
=1-1+
| 1 |
| 729 |
=
| 1 |
| 729 |
点评:此题经过变形后,每个分数能够拆分成两个分数相减的形式,相互抵消,即可得出结果.
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