问题 选择题
乘积(1-
1
22
)(1-
1
32
)(1-
1
42
)…(1-
1
19982
)(1-
1
19992
)(1-
1
20002
)
等于(  )
A.
1999
2000
B.
2001
2000
C.
1999
4000
D.
2001
4000
答案

原式=(1-

1
2
)(1+
1
2
)(1-
1
3
)(1+
1
3
)(1-
1
4
)(1+
1
4
)…(1-
1
1998
)(1+
1
1998
)(1-
1
1999
)(1+
1
1999
)(1-
1
2000
)(1+
1
2000
),

=

1
2
×
3
2
×
2
3
×
4
3
×
3
4
×
5
4
×…×
1997
1998
×
1999
1998
×
1998
1999
×
2000
1999
×
1999
2000
×
2001
2000

=

1
2
×
2001
2000

=

2001
4000

故选D.

单项选择题
单项选择题