Java语言程序计划基础篇_编程练习题18.4 (对数列求和)

题目：18.4 (对数列求和)

编写一个递归方法来盘算下面的级数:

编写一个测试程序，为i = 1, 2, …, 10显示m(i)

• 代码示例
  

   编程练习题18_4SumOfSequences.java 

1. package chapter_18;
3. public class 编程练习题18_4SumOfSequences {
4.         public static void main(String[] args) {
5.                 for(int i = 1;i <= 10;i++) {//从1到10
6.                         System.out.printf("When i is %d, the sum of the fraction is %.2f\n",i,sequences(i));
7.                 }
8.         }
9.         public static double sequences(int n) {
10.                 return sequences(1,n);
11.         }
12.        
13.         public static double sequences(int i,int n) {
14.                 if(i > n)// 如果i大于n，说明已经超出了范围，返回0（因为没有元素可加）  
15.                         return 0;
16.                 else return 1.0/i + sequences(i+1, n);// 否则，返回当前数的倒数加上从i+1到n的倒数之和  
17.         }
19. }

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• 输出结果
  

1. When i is 1, the sum of the fraction is 1.00
2. When i is 2, the sum of the fraction is 1.50
3. When i is 3, the sum of the fraction is 1.83
4. When i is 4, the sum of the fraction is 2.08
5. When i is 5, the sum of the fraction is 2.28
6. When i is 6, the sum of the fraction is 2.45
7. When i is 7, the sum of the fraction is 2.59
8. When i is 8, the sum of the fraction is 2.72
9. When i is 9, the sum of the fraction is 2.83
10. When i is 10, the sum of the fraction is 2.93

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