Question

已知數(shù)列

1

6

，

1

12

，

1

20

，…，

1

(n+1)(n+2)

…，則其前n項和S_n=______．

Answer 1

設(shè)數(shù)列為{a_n}則由題意可得：
數(shù)列的通項公式為an =

1

(n+1)(n+2)

=

1

n+1

-

1

n+2

．
所以S_n=a₁+a₂+…+a_n
=

1

2

-

1

3

+

1

3

-

1

4

+… +

1

n+1

-

1

n+2

=

1

2

-

1

n+2

=

2

2(n+2)

．
故答案為

2

2(n+2)

．