杭电1012

u Calculate e

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 40284    Accepted Submission(s): 18307

Problem Description

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.

 

Sample Output

   
   
   
   

    
    
    
    n e
- -----------
0 1
1 2
2 2.5
3 2.666666667
4 2.708333333
   
   
   
   

 

#include <iostream>
#include <iomanip>
using namespace std;
double fun(double j)
{
    double sum=1;
    for(int i=1;i<=j;i++)
    {
        sum=sum*i;
    }
    return sum;
}
int main()
{
    double sum=0;
    cout<<"n"<<" "<<"e"<<endl;
    cout<<"-"<<" "<<"-----------"<<endl;
    cout<<0<<" "<<1<<endl;
    cout<<1<<" "<<2<<endl;
    cout<<2<<" "<<2.5<<endl;
    for(int i=3;i<=9;i++)
    {
        for(int j=0;j<=i;j++)
        {
            if(j==0)
            {
                sum=1;
            }
            else
            {
                sum=1/fun(j)+sum;
            }
        }

        cout<<i<<" "<<setiosflags(ios::fixed)<<setprecision(9)<<sum<<endl;
        sum=0;
    }
    return 0;
}