问题 填空题
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
=______,1-
1
20132
=______.
答案

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

单项选择题
单项选择题