A simple mathematical formula for e is

where n is allowed to go to infinity. This can actually yield very accurate approximations of e using relatively small values of n.
Output Output the approximations of e generated by the above formula for the values of n from 0 to 9. The beginning of your output should appear similar to that shown below. where n is allowed to go to infinity. This can actually yield very accurate approximations of e using relatively small values of n.
Sample Output
n e
- -----------
0 1
1 2
2 2.5
3 2.666666667
4 2.708333333
#include<iostream>
#include<stdlib.h>
#include<cmath>
#include<cstring>
using namespace std;
long long mi(int l){
if(l==0)
return 1;
long long num=1;
for(int i=1;i<=l;i++)
{
num=num*i;
}
return num;
}
int main(){
double e=0
;cout<<"n e"<<endl;
cout<<"- -----------"<<endl;
for(int i=0;i<=2;i++) {
e=e+1.0/mi(i);
cout<<i<<" "<<e<<endl;
}
for(int i=3;i<=9;i++)
{
e=e+1.0/mi(i);
printf("%d %.9lf\n",i,e);
}
return 0;
}

本文介绍了一种通过数学公式计算自然对数的底数e的近似值的方法,并使用C++实现了一个程序来展示如何随着迭代次数增加,逐步提高e的计算精度。输出结果从n为0到9的范围内展示了不同阶乘项对总和的贡献。
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