观察下列计算:11×2=1-1212×3=12-1313×4=13-1414×5=14-15…从计算结果中找规律,利用规律性计算11×2+12×3+13×4+14×5…+12009×2010=____

题目简介

观察下列计算:11×2=1-1212×3=12-1313×4=13-1414×5=14-15…从计算结果中找规律,利用规律性计算11×2+12×3+13×4+14×5…+12009×2010=____

题目详情

观察下列计算:
1
1×2
=1-
1
2
1
2×3
=
1
2
-
1
3
1
3×4
=
1
3
-
1
4
1
4×5
=
1
4
-
1
5


从计算结果中找规律,利用规律性计算
1
1×2
+
1
2×3
+
1
3×4
+
1
4×5
…+
1
2009×2010
=______.
题型:填空题难度:中档来源:荆门

答案


class="stub"1
1×2
=1-class="stub"1
2

class="stub"1
2×3
=class="stub"1
2
-class="stub"1
3

class="stub"1
3×4
=class="stub"1
3
-class="stub"1
4

class="stub"1
4×5
=class="stub"1
4
-class="stub"1
5

…;
class="stub"1
2009×2010
=class="stub"1
2009
-class="stub"1
2010

class="stub"1
1×2
+class="stub"1
2×3
+class="stub"1
3×4
+class="stub"1
4×5
…+class="stub"1
2009×2010

=(1-class="stub"1
2
)+(class="stub"1
2
-class="stub"1
3
)+(class="stub"1
3
-class="stub"1
4
)+(class="stub"1
4
-class="stub"1
5
)+…+(class="stub"1
2009
-class="stub"1
2010

=1-class="stub"1
2010
=class="stub"2009
2010

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