题目内容
(2012?北京模拟)
+
+
+
+
+
+
.
| 1 |
| 12 |
| 1 |
| 20 |
| 1 |
| 30 |
| 1 |
| 42 |
| 1 |
| 56 |
| 1 |
| 72 |
| 1 |
| 90 |
分析:
=
-
,
=
-
,
=
-
…
由此进行化简求解.
| 1 |
| 12 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 20 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 30 |
| 1 |
| 5 |
| 1 |
| 6 |
…
由此进行化简求解.
解答:解:
+
+
+
+
+
+
,
=(
-
)+(
-
)+(
-
)+…+(
-
),
=
-
+
-
+
-
+…+
-
,
=
-
,
=
.
| 1 |
| 12 |
| 1 |
| 20 |
| 1 |
| 30 |
| 1 |
| 42 |
| 1 |
| 56 |
| 1 |
| 72 |
| 1 |
| 90 |
=(
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 5 |
| 1 |
| 6 |
| 1 |
| 9 |
| 1 |
| 10 |
=
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 5 |
| 1 |
| 6 |
| 1 |
| 9 |
| 1 |
| 10 |
=
| 1 |
| 3 |
| 1 |
| 10 |
=
| 7 |
| 30 |
点评:本题通过分数裂项,找出化简的方法,进而求解.
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