Question

若对任意的自然数n，Sn=

1

1×2

+

1

2×3

+

1

3×4

+…+

1

n×(n+1)

=

10

11

，则n=______．

Answer 1

Sn=

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

=

10

11

所以，n=10
故答案为：10