OJ 1129 fraction matrix

describe

We define the matrix as follows ：
1/1 1/2 1/3
1/2 1/1 1/2
1/3 1/2 1/1
The elements on the diagonal of a matrix are always 1/1, The denominators of the fractions on both sides of the diagonal increase one by one .
Request the sum of this matrix .

Input
Input contains multiple sets of test data . Given integer per line N（N<50000）, The representation matrix is N*N. When N=0 when , End of input .

Output
Output the answer , The result is reserved 2 Decimal place .

sample input 1 

1
2
3
4
0
sample output 1

1.00
3.00
5.67
8.83

The topic is regular , First of all, on both sides of the diagonal are symmetry Of , also Quantity is decreasing Of , Denominator from 1~n The quantity is just decreasing , also The difference between two adjacent denominators 1, On the other side 1~1/n The number of n~1, Because of symmetry, we have to multiply everything except diagonal 2, That is, the number of data outside the diagonal is （n-i）*2, According to this rule, we can get the result .

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

int main()
{
    int n;
    while(cin>>n&&n)
    {
        double sum=n;
        for(int i=1;i<n;i++)
            {
                sum+=((n-i)*2.0)/(i+1.0);
            }
            printf("%.2f\n",sum);
    }
    return 0;
}