问题
解答题
观察下列各式及验证过程:
(1)按照上述两个等式及其验证过程的基本思路,猜想
(2)针对上述各式反映的规律,写出用n(n为大于等于2的整数)表示的等式,并进行验证. |
答案
(1)
=
(1 4
-1 5
)1 6 1 5 5 24
验证:左边=
=1 4×5×6
=5 4×52×6 1 5
=右边,故正确;5 24
(2)
=
(1 n
-1 n+1
)1 n+2 1 n+1 n+1 n(n+2)
验证:左边=
=n+1 n(n+1)(n+2)
=n+1 n(n+1)2(n+2) 1 n+1
=右边n+1 n(n+2)
故正确.