题目内容
(2-1÷2)×(2-2÷3)×(2-3÷4)×(2-4÷5)×…×(2-2003÷2004)=分析:把除法用分数表示,即原式=(2-
)×(2-
)×(2-
)×(2-
)×…×(2-
),算出每个括号内的结果,然后相乘,注意约分.
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| 2 |
| 2 |
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| 3 |
| 4 |
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| 5 |
| 2003 |
| 2004 |
解答:解:(2-1÷2)×(2-2÷3)×(2-3÷4)×(2-4÷5)×…×(2-2003÷2004),
=(2-
)×(2-
)×(2-
)×(2-
)×…×(2-
),
=
×
×
×
×…×
,
=
×2005,
=1002.5.
=(2-
| 1 |
| 2 |
| 2 |
| 3 |
| 3 |
| 4 |
| 4 |
| 5 |
| 2003 |
| 2004 |
=
| 3 |
| 2 |
| 4 |
| 3 |
| 5 |
| 4 |
| 6 |
| 5 |
| 2005 |
| 2004 |
=
| 1 |
| 2 |
=1002.5.
点评:解答此题,应注意审题,采取巧妙的方法,通过约分进行简算.
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