HDU 2156 分数矩阵

#include <bits/stdc++.h>
using namespace std;

double a[55555];

int main() {
    a[0] = 0, a[1] = 1, a[2] = 3;
    for(int i = 3; i <= 50001; i ++) {
        a[i] = 2 * a[i - 1] - a[i - 2] + 2.0 / i;
    }

    int N;
    while(~scanf("%d", &N)) {
        if(N == 0) break;
        printf("%.2lf\n", a[N]);
    }
    return 0;
}