但是当我输入一个10位数的数字时,公式和迭代方法会给出单独的答案.

我试图在谷歌上查找但无法找到任何解决方案.我的代码：

#include <bits/stdc++.h>
using namespace std;

int main(){

    unsigned long long i,n,sum = 0,out_put;
    cout << "Sum of numbers from 1 to: ";
    cin >> n;

    /// using mathematical formula
    out_put = n*(n+1);
    out_put = out_put/2;
    cout << " =   " << out_put << endl;

    /// using iteration
    for (i=1; i<=n; i++){
        sum = sum+i;
    }
    cout << " ==  " << sum << endl;

    return 0;
}

怎么知道哪一个是正确的？如果我假设公式不能错,那么为什么迭代方法给出错误答案？我用unsigned long long来防止溢出但仍然无法正常工作.