Question

如果

1

2

+

1

6

+

1

12

+…+

1

n(n+1)

=

2011

2012

，那么n=______．

Answer 1

1

2

+

1

6

+

1

12

+…+

1

n(n+1)

=1-

1

2

+

1

2

-

1

3

+

1

3

-

1

4

+…+

1

n

-

1

n+1

=1-

1

n+1

=

n

n+1

所以，

n

n+1

=

2011

2012

2012n=2011n+2011
n=2011
故答案为：2011．