用c++编写程序，求e的近似值，直到最后一项的绝对值小于10-5为止，输出保留5位小数。（要求用do- while和while两种方法） e=1+1/1!+1/2!+1/3!+1/4!+...+1/n!

用C++编写程序计算e的近似值并保留5位小数，可以使用do-while和while循环结构分别实现。这里我们假设有一个函数`factorial`用于计算阶乘。以下是两个版本的示例：

**do-while循环版本**:

#include <iostream>
#include <cmath>
using namespace std;

double factorial(int n) {
    if (n == 0 || n == 1)
        return 1;
    else
        return n * factorial(n - 1);
}

double calculate_e_do_while(double current_sum, int n, double threshold = pow(10, -5)) {
    double term = 1.0 / factorial(n);
    do {
        current_sum += term;
        n++;
        term /= n;
    } while (abs(term) >= threshold);
    return round(current_sum * 100000) / 100000.0; // 输出保留5位小数
}

int main() {
    double e_approximation = calculate_e_do_while(1.0, 1);
    cout << "e的近似值 (do-while): " << fixed << setprecision(5) << e_approximation << endl;
    return 0;
}

**while循环版本**:

#include <iostream>
#include <cmath>
using namespace std;

// 同上

double calculate_e_while(double current_sum, int n, double threshold = pow(10, -5)) {
    double term = 1.0 / factorial(n);
    while (abs(term) >= threshold) {
        current_sum += term;
        n++;
        term /= n;
    }
    return round(current_sum * 100000) / 100000.0; // 输出保留5位小数
}

int main() {
    double e_approximation = calculate_e_while(1.0, 1);
    cout << "e的近似值 (while): " << fixed << setprecision(5) << e_approximation << endl;
    return 0;
}