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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)