观察下列各式:1-122=12×32;1-132=23×43;1-142=34×54.…根据上面的等式所反映的规律,填空:1-1502=______,1-120132=______.-数学

题目简介

观察下列各式:1-122=12×32;1-132=23×43;1-142=34×54.…根据上面的等式所反映的规律,填空:1-1502=______,1-120132=______.-数学

题目详情

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
=______.
题型:填空题难度:偏易来源:不详

答案

1-class="stub"1
22
=class="stub"1
2
×class="stub"3
2
=(1-class="stub"1
2
)(1+class="stub"1
2
);1-class="stub"1
32
=class="stub"2
3
×class="stub"4
3
=(1-class="stub"1
3
)(1+class="stub"1
3
);1-class="stub"1
42
=class="stub"3
4
×class="stub"5
4
=(1-class="stub"1
4
)(1+class="stub"1
4
).…
∴1-class="stub"1
502
=(1-class="stub"1
50
)(1+class="stub"1
50
)=class="stub"49
50
×class="stub"51
50

1-class="stub"1
20132
=(1-class="stub"1
2013
)(1+class="stub"1
2013
)=class="stub"2012
2013
×class="stub"2014
2013

故答案为:class="stub"49
50
×class="stub"51
50
class="stub"2012
2013
×class="stub"2014
2013

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