Question

觀察下列計(jì)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

…
從計(jì)算結(jié)果找規(guī)律，利用規(guī)律計(jì)算

1

1×2

+

1

2×3

+

1

3×4

+

1

4×5

+…+

1

2013×2014

=

 

．

Answer 1

考點(diǎn)：規(guī)律型：數(shù)字的變化類

專題：規(guī)律型

分析：根據(jù)計(jì)算規(guī)律，相鄰兩個(gè)數(shù)的乘積的倒數(shù)等于它們的倒數(shù)的差，然后裂項(xiàng)計(jì)算即可得解．

解答：解：

1

1×2

+

1

2×3

+

1

3×4

+

1

4×5

+…+

1

2013×2014

=1-

1

2

+

1

2

-

1

3

+

1

3

-

1

4

+

1

4

-

1

5

+…+

1

2013

-

1

2014

=1-

1

2014

=

2013

2014

．
故答案為：

2013

2014

．

點(diǎn)評(píng)：本題是對(duì)數(shù)字變化規(guī)律的考查，仔細(xì)觀察規(guī)律，正確裂項(xiàng)是解題的關(guān)鍵．