HDU 1012 u Calculate e

u Calculate e

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 40656    Accepted Submission(s): 18488

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
   
   
   
   

 

Source

Greater New York 2000

 

#include<stdio.h>
double sum(int a)
{
    int aa=1;
    for(int i=1; i<=a; i++)
    {
        aa*=i;
    }
    return (double)1.0/aa;
}
int main (void)
{
    double a[11];
    printf("n e\n");
    printf("- -----------\n");

    printf("0 1\n");
    printf("1 2\n");
    printf("2 2.5\n");
    a[0]=1;
    a[1]=2;
    for(int i=2; i<=9; i++)
    {
        a[i]=a[i-1]+sum(i);
        if(i>=3)
            printf("%d %.9lf\n",i,a[i]);
    }
    return 0;
}