Question

观察算式： 1 1×2 =1- 1 2 = 1 2

Answer 1

（1）按规律填空

1

1×2 +

1

2×3 +

1

3×4 +

1

4×5 +

1

5×6 =1-

1

2 +

1

2 -

1

3 +

1

3 -

1

4 +

1

4 -

1

5 +

1

5 -

1

6 =1-

1

6 =

5

6 ，

1

1×2 +

1

2×3 +

1

3×4 +

1

4×5 +…+

1

99×100 =1-

1

100 =

99

100 ；

（2）

1

n(n+1) +

1

(n+1)(n+2) +

1

(n+2)(n+3) +

1

(n+3)(n+4) +…+

1

(n+99)(n+100)

=

1

n -

1

n+1 +

1

n+1 -

1

n+2 +…+

1

n+99 -

1

n+100

=

1

n -

1

n+100 ．