小白求问大佬们为什么一开始n设为int会超时，改成double就可以了？

import java.util.Scanner;

public class P1035 {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		double Sn = 0;
		int k = scanner.nextInt();
	
		for (double n = 1.0; Sn <= k; n ++) {
			Sn += 1/n;
			if (Sn >= k) {
				System.out.println((int) n);
				return;
			}
		}
		scanner.close();
	}
}