问题 填空题
观察下列各式:
1+
1
3
=2
1
3
2+
1
4
=3
1
4
3+
1
5
=4
1
5
…,请你将猜想:
(1)
4+
1
6
=______,
5+
1
7
=______.
(2)请你将猜想到的规律用含有自然数n(n≥1)的代数式表达出来.
答案

(1)∵

1+
1
3
=2
1
3
2+
1
4
=3
1
4
3+
1
5
=4
1
5
…,

4+
1
6
=5
1
6
5+
1
7
=6
1
7

故答案为:5

1
6
,6
1
7

(2)∵

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

∴规律为:

n+
1
n+2
=(n+1)
1
n+2
(n≥1).

单项选择题
单项选择题