问题 解答题
(1+
1
2
)×(1-
1
2
)×(1+
1
3
)×(1-
1
3
)×…×(1+
1
99
)×(1-
1
99
)
等于______.
答案

(1+

1
2
)×(1-
1
2
)×(1+
1
3
)×(1-
1
3
)×…×(1+
1
99
)×(1-
1
99
),

=[(1+

1
2
)×(1+
1
3
)×…×(1+
1
99
)]×[(1-
1
2
)×(1-
1
3
)×…×(1-
1
99
)],

=[

3
2
×
4
3
×…×
100
99
]×[
1
2
×
2
3
×…×
98
99
],

=

100
2
×
1
99

=

50
99

故答案为:

50
99

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