作业帮找规律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（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)]
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/05 18:30:27
![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（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)]](/uploads/image/z/7160808-48-8.jpg?t=%E6%89%BE%E8%A7%84%E5%BE%8B1%2F2%3D1%2F1%C3%971%2F2%3D1%2F1-1%2F2%3B1%2F6%3D1%2F%282%C3%973%29%3D1%2F2-1%2F3%3B1%2F12%3D1%283%C3%974%29%3D1%2F3-1%2F4%281%29%E7%94%A8%E5%90%ABn%EF%BC%88n%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%EF%BC%89%E7%9A%84%E7%AD%89%E5%BC%8F%E8%A1%A8%E7%A4%BA%EF%BC%882%EF%BC%89%E7%94%A8%E5%BE%97%E5%88%B0%E7%9A%84%E7%BB%93%E8%AE%BA%E8%AE%A1%E7%AE%97%5B1%2F%28a-1%29%28a-2%29%5D%2B%5B1%2F%28a-2%29%28a-3%29%5D%2B%5B1%2F%28a-3%29%28a-4%29%5D%2B%5B1%2F%28a-4%29%28a-5%29%5D)
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（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)]
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
（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)]
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（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)]