题目内容
(1-
)×(1-
)×(1-
)×…×(1-
)= .
1 |
2×2 |
1 |
3×3 |
1 |
4×4 |
1 |
11×11 |
考点:分数的巧算
专题:计算问题(巧算速算)
分析:运用平方差公式,因为1-
=(1-
)×(1+
),1-
=(1-
)×(1+
),…,1-
=(1-
)×(1+
),求出每个括号内的数,约分计算.
1 |
2×2 |
1 |
2 |
1 |
2 |
1 |
3×3 |
1 |
3 |
1 |
3 |
1 |
11×11 |
1 |
11 |
1 |
11 |
解答:
解:(1-
)×(1-
)×(1-
)×…×(1-
)
=(1-
)×(1+
)×(1-
)×(1+
)×(1-
)×(1+
)×…(1-
)×(1+
)
=
×
×
×
×
×
×…×
×
=
×
=
故答案为:
.
1 |
2×2 |
1 |
3×3 |
1 |
4×4 |
1 |
11×11 |
=(1-
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
4 |
1 |
4 |
1 |
11 |
1 |
11 |
=
1 |
2 |
3 |
2 |
2 |
3 |
4 |
3 |
3 |
4 |
5 |
4 |
9 |
10 |
11 |
10 |
=
1 |
2 |
11 |
10 |
=
11 |
20 |
故答案为:
11 |
20 |
点评:认真分析数据,运用运算技巧,灵活简算.
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