题目： 2/1, 3/2, 5/3, 8/5, 13/8, 21 13 ...

java源码：

package studying;

import java.util.Scanner;

public class Sum_Of_FirstN {

    /*
     * Topic: There is a score sequence: 2/1, 3/2, 5/3, 8/5, 13/8, 21 13 ...
     * find the sum of the first 20 of this series.
     */

    public static void main(String[] args) {

        Scanner input = new Scanner(System.in);
        System.out.println("Please enter n :");
        int n = input.nextInt();

        double a = 2;
        double b = 1;
        double sum = 0;
        double t;

        for(int i = 1; i <= n; i++) {
            sum += a/b;  //this is key point.
            t = a;
            a = a + b;
            b = t;
        }
        System.out.println("The sum of the first n of the sequence:\n" + sum);
    }

}

结果展示：