初一。找规律

1/2=1/1×1/2=1/1-1/2; 1/6=1/(2×3)=1/2-1/3; 1/12=1(3×4)=1/3-1/4

(1）用含n（n为正整数）的等式表示:

1/[n * (n + 1)] = 1/n - 1/(n+1) 或者
1/[(n - 1) * n] = 1/(n - 1) - 1/n

(2)用得到的结论计算:

[1/(a-1)(a-2)]+[1/(a-2)(a-3)]+[1/(a-3)(a-4)]+[1/(a-4)(a-5)]

= [1/(a-2) - 1/(a-1)] + [1/(a-3) - 1/(a-2)] + [1/(a-4) - 1/(a-3)] + [1/(a-5) - 1/(a-4)]

= 1/(a-2) - 1/(a-1) + 1/(a-3) - 1/(a-2) + 1/(a-4) - 1/(a-3) + 1/(a-5) - 1/(a-4)

= 1/(a-5) - 1/(a-1)

= 4/[(a-1)(a-5)]

(1)1/[n(n+1)]=1/n-1/n+1
(2)[1/a-2]-[1/a-1]......=[1/a-5]-[1/a-1]