问题 解答题
(1)观察下列各式:
2-
2
5
=
8
5
=
4×2
5
=2
2
5
,即
2-
2
5
=2
2
5
3-
3
10
=
27
10
=
9×3
10
=3
3
10
,即
3-
3
10
=3
3
10

(2)按照上式所含的规律,根据你的理解填写:
4-
4
17
=______=______=______,即
4-
4
17
=______.
(3)猜想
5-
5
26
=______.
(4)请你用含有自然数n(n≥2)的式子写出你发现的规律,并给出检证过程.
答案

(2)

4-
4
17
=
64
17
=
16×4
17
=4
4
17

4-
4
17
=4
4
17

(3)

5-
5
26
=5
5
26

(4)

n-
n
n2+1
=n
n
n2+1

n-
n
n2+1

=

n(n2+1)-n
n2+1

=

n(n2+1-1)
n2+1

=

n2
n2+1

=n

n
n2+1

单项选择题
单项选择题