问题 解答题
计算:(1-
1
22
)(1-
1
32
)…(1-
1
92
)(1-
1
102
)=______
答案

(1-

1
22
)(1-
1
32
)…(1-
1
92
)(1-
1
102
),

=(1-

1
2
)(1+
1
2
)(1-
1
3
)(1+
1
3
)•…•(1-
1
9
)(1+
1
9
)(1-
1
10
)(1+
1
10
),

=

1
2
×
3
2
×
2
3
×
4
3
×
3
4
×
5
4
×…×
8
9
×
10
9
×
9
10
×
11
10

=

1
2
×
11
10

=

11
20

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