问题 解答题
观察下列各式的计算结果
1-
1
22
=1-
1
4
=
3
4
=
1
2
×
3
2

1-
1
32
=1-
1
9
=
8
9
=
2
3
×
4
3

1-
1
42
=1-
1
16
=
15
16
=
3
4
×
5
4

1-
1
52
=1-
1
25
=
24
25
=
4
5
×
6
5


(1)用你发现的规律填写下列式子的结果:
1-
1
62
=______×______
1-
1
1002
=______×______
(2)用你发现的规律计算:
(1-
1
22
)×(1-
1
32
)×(1-
1
42
)×…×(1-
1
20122
)×(1-
1
20132
)
答案

(1)1-

1
62
=1-
1
36
=
35
36
=
5
6
×
7
6

1-

1
1002
=1-
1
10000
=
9999
10000
=
99
100
×
101
100

(2)根据题意得:原式=

1
2
×
3
2
×
2
3
×
4
3
×
3
4
×
5
4
×
4
5
×
6
5
×…×
2012
2013
×
2014
2013

=

1007
2013

故答案为:

5
6
7
6
99
100
101
100

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