试题

题目:
观察下列各式:
1-
1
22
=
1
2
×
3
2
1-
1
32
=
2
3
×
4
3
1-
1
42
=
3
4
×
5
4
.…
根据上面的等式所反映的规律,填空:1-
1
502
=
49
50
×
51
50
49
50
×
51
50
1-
1
20132
=
2012
2013
×
2014
2013
2012
2013
×
2014
2013

答案
49
50
×
51
50

2012
2013
×
2014
2013

解:∵1-
1
22
=
1
2
×
3
2
=(1-
1
2
)(1+
1
2
);1-
1
32
=
2
3
×
4
3
=(1-
1
3
)(1+
1
3
);1-
1
42
=
3
4
×
5
4
=(1-
1
4
)(1+
1
4
).…
∴1-
1
502
=(1-
1
50
)(1+
1
50
)=
49
50
×
51
50

1-
1
20132
=(1-
1
2013
)(1+
1
2013
)=
2012
2013
×
2014
2013

故答案为:
49
50
×
51
50
2012
2013
×
2014
2013
考点梳理
规律型:数字的变化类.
根据已知数据得出规律,1-
1
n2
=(1-
1
n
)(1+
1
n
)进而求出即可.
此题主要考查了数字变化规律,根据已知数据得出数字的变与不变是解题关键.
找相似题