https://www.luogu.com.cn/problem/P4550

#include<bits/stdc++.h>
using namespace std;
const int N=2e5+10;
double num[N],ans[N];
int main()
{
    int n;
    cin>>n;
    num[n]=0;
    ans[n]=0;
    for(int i=n-1;i>=0;i--)
    {
        double p1=(double)i/n,p2=(double)(n-i)/n;
      //  cout<<i<<"  "<<n<<"    "<<p1<<"     "<<p2<<endl;
        num[i]=(p2*num[i+1]+1)/(1-p1);
        ans[i]=(ans[i+1]*p2+num[i]*p1+num[i+1]*p2+1)/(1-p1);

    }
    printf("%.2lf",ans[0]);
}