初一。找规律
来源:百度知道 编辑:UC知道 时间:2024/09/22 16:43:13
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
(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)用含n(n为正整数)的等式表示
(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)]
1/2=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]