问题 解答题
观察下列各式:
1+
1
3
=2
1
3

2+
1
4
=3
1
4

3+
1
5
=4
1
5


(1)请你猜想:
4+
1
6
=______
(2)请你写出第10个式子是:______,并写出推导的过程.
(3)根据你观察到的规律,请你写出第n个式子是:______.
答案

(1)

4+
1
6
=
25
6
=5
1
6

故答案为:5

1
6

(2)

10+
1
12
=
121
12
=11
1
12

故答案为:

10+
1
12
=11
1
12

(3)

n+
1
n+2
=
n(n+2)+1
n+2
=
(n+1)2
n+2
=(n+1)
1
n+2

故答案为:

n+
1
n+2
=(n+1)
1
n+2

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