> 数学 >
计算(1−
1
22
)(1−
1
32
)…(1−
1
92
)(1−
1
102
)
=(  )
A.
10
21

B.
13
21

C.
9
20

D.
11
20
人气:165 ℃ 时间:2020-03-02 06:25:45
解答
原式=(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
×…×
8
9
×
10
9
×
9
10
×
11
10

=
11
20

故选D.
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