11•2+12•3+…+1n(n+1)=______．

题型：不详难度：来源：

1

1•2

+

1

2•3

+…+

1

n(n+1)

=______．

答案

∵

1

n(n+1)

=

1

n

-

1

n+1

∴

1

1•2

+

1

2•3

+…

1

n(n+1)

=1-

1

2

+

1

2

-

1

3

+…+

1

n

-

1

n+1

=1-

1

n+1

=

n

n+1

故答案为：

n

n+1