问题 解答题
用简便方法计算
(1)20102-2011×2009
(2)(1-
1
22
)(1-
1
32
)(1-
1
42
)…(1-
1
92
)(1-
1
102
答案

(1)原式=20102-(2010+1)

=20102-(20102-1)

=20102-20102+1

=1;

(2)原式=(1-

1
2
)(1+
1
2
)(1-
1
3
)(1+
1
3
)(1-
1
4
)(1+
1
4
)…(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
×
9
10
×
11
10

=

1
2
×
11
10

=

11
20

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