1(x+1)(x+2)+1(x+2)(x+3)+…+1(x+2006)(x+2007)=______

题型：填空题难度：一般来源：不详

1

(x+1)(x+2)

+

1

(x+2)(x+3)

+…+

1

(x+2006)(x+2007)

=______

答案

原式=

1

x+1

-

1

x+2

+

1

x+2

-

1

x+3

+…+

1

x+2006

-

1

x+2007

=

1

x+1

-

1

x+2007

=

2006

(x+1)(x+2007)

．