求下列多项式前k项的和，1 - 1/2 + 2/3 - 3/4 +4/5 - 5/6 + ... 要求结果表示为真分式形式Java

public class Main {
    public static void main(String[] args) {
        double a = 1, b = 2, sum = 0;
        double t = a / (b * b);
        double n;
        int i;
        // 请在此处输入n的值
        n = 10;
        for (i = 1; i <= (n - 1); i++) {
            a = a + 1;
            b = b + 1;
            t = a / (b * b);
            sum += t;
        }
        System.out.println(1 - sum);
    }
}