英文数学题求救,分数类的!
问题描述：
英文数学题求救,分数类的!
A find the decimal expamsion for 1/43
B show that 9 is a factor of the sum of the digits in the repetend of 1/7.1/39,1/43
C suppose none of 2,3,5 is a factor of n.Explain why 9 is a factor of the sum ofthe digits in the repetend in the repetend of 1/n
D Find the fourth smallest value of n which neither 2 nor 5 is a factor and 9 is not a factor of the sum of the digits in the repetend of 1/n
求C 和
答
D：根据C的结论,n必须是3的幂,也就是3,9,27,81? 是81吗能回答c就给满意答案了，谢谢 假设1/n化成小数后 从第k+1位开始循环，循环节长度是s，即1/n=0.x1……xk a1……as a1……as ……，则1/n=x/(10^k)+(a1……as)/(10^k * 99……9)一共s个9； 于是1/n=(x*99……9+a1……as)/(10^k * 99……9)，于是可得： (x*99……9+a1……as) * n=10^k * 99……9，等式右边能被9整除，而n不能被3整除，因此x*99……9+a1……as能被9整除； 得a1……as能被9整除； 则9也整除a1+a2+……as