Question

若 S n = 1 1•2 + 1 2•3 + 1 3•4 …+ 1 n•(n+1) (n∈ N * ) ，则S 10

Answer 1

∵ S n =

1

1•2 +

1

2•3 +

1

3•4 +…+

1

n(n+1)

= 1-

1

2 +

1

2 -

1

3 +…+

1

n -

1

n+1

= 1-

1

n+1 =

n

n+1

∴ S 10 =

10

11

故选C．