无穷级数求和：区间内的分数方程求解教程

import java.util.Scanner;

public class InfiniteSeriesSum {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.print("x=");
        double x = sc.nextDouble();
        sc.close();

        if (x < 0.1 || x > 1.5) {
            System.out.println("error");
            return;
        }

        double i = 2; // 使用 double 类型，避免整数除法
        int neg = -1;
        double pow;
        double pow_res;
        double res = 0;
        double loop_check = 1;

        while (Math.abs(loop_check) > 0.0001 || i < 100) { // 增加最大迭代次数，避免死循环
            pow = i;
            pow_res = 1;
            for(int j = 0; j < pow; j++){
              pow_res *= 2 * x;
            }
            loop_check = pow_res / factorial(i); // 计算当前项的值，并用于循环条件判断
            res = res + neg * loop_check;
            i = i + 2;
            neg = -neg;
        }
        System.out.printf("function=%.4f%n", 2 * (Math.cos(x) * Math.cos(x) - 1));
        System.out.printf("summa=%.4f%n", -res);
    }

    // 阶乘函数
    public static double factorial(double n) {
        if (n == 0) {
            return 1;
        } else {
            return n * factorial(n - 1);
        }
    }
}