Question

计算：1×

1

1× 1 1× 1 1× 1 1× 1 1 +1 +1 +1 +1

+1=

 

．

Answer 1

考点：繁分数的化简

专题：计算问题（巧算速算）

分析：此题设计新颖，通过仔细观察，从下往上逐步计算，进而得出结果．

解答： 解：1×

1

1× 1 1× 1 1× 1 1× 1 1 +1 +1 +1 +1

+1
=1×

1

1× 1 1× 1 1× 1 1+1 +1 +1 +1

+1
=1×

1

1× 1 1× 1 3 2 +1 +1

+1
=1×

1

1× 1 1× 2 3 +1 +1

+1
=1×

1

1× 1 5 3 +1

+1
=1×

1

3 5 +1

+1
=1×

1

8 5

+1
=1×

5

8

+1
=

5

8

+1
=

13

8

故答案为：

13

8

．

点评：此题设计新颖，构思巧妙，应仔细观察，抓住特点，巧妙解答．