用递归求分数的和

import java.io.IOException;
import java.util.Scanner;

public class Sum {
    public static void main(String[] args) throws IOException {
        try {
            System.out.println("请输入的i的值！");
            Scanner input = new Scanner(System.in);
            int i = input.nextInt();
            System.out.println("求和的值为：" + sum(i));
        } catch (Exception ex) {
            System.out.println("输入的i为整数！");
        }
    }

    public static double sum(int i) {
        double result = 0;
        int j;
        for (j = i; j > 0; j--) {
            result = result + ((double) j / (2 * (double) j + 1));
        }
        System.out.println("输入的整数要求为正！");
        return result;
    }
}

递归求和m(i)=i/(i*2+1)