Sum of averages

#include <bits/stdc++.h>
#define f(i,a,b) for(int i = (a); i <= (b); i++)

using namespace std;

double F[100005], S[100005];
int A[100005], N;

int main()
{
    cin >> N;
    f(i,1,N) scanf("%d", &A[i]);

    S[1] = 1;
    f(i,2,100000) S[i] = S[i-1] + (1.0 / i);

    int a = 1, b = N;
    while(a <= b)
    {
        F[a] = F[a-1] + S[b] - S[a-1];
        F[b] = F[b+1] + S[b] - S[a-1];
        a++, b--;
    }

    double ans = 0;
    f(i,1,N) ans += F[i] * A[i];

    cout << setprecision(6) << fixed << ans << "\n";
}