问题
填空题
观察下列各式:
(1)
(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)∵
=21+ 1 3
;1 3
=32+ 1 4
;1 4
=43+ 1 5
…,1 5
∴
=54+ 1 6
,1 6
=65+ 1 7
;1 7
故答案为:5
,61 6
;1 7
(2)∵
=n+ 1 n+2
=n(n+2)+1 n+2
=(n+1)(n+1)2 n+2
.1 n+2
∴规律为:
=(n+1)n+ 1 n+2
(n≥1).1 n+2