#include <bits/stdc++.h>

using namespace std;

inline int toInt(string s) {int v; istringstream sin(s);sin>>v;return v;}
template<class T> inline string toString(T x) {ostringstream sout;sout<<x;return sout.str();}
template<class T> inline T sqr(T x) {return x*x;}

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<string> vs;
typedef pair<int, int> pii;
typedef long long ll;

#define all(a)  (a).begin(),(a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define pb push_back
#define mp make_pair
#define each(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define exist(s,e) ((s).find(e)!=(s).end())
#define range(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)  range(i,0,n)
#define clr(a,b) memset((a), (b) ,sizeof(a))
#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;

const double eps = 1e-15;
const double pi  = acos(-1.0);
const ll INF =1LL << 62;
const int inf =1 << 29;


const int nmax=100000;
double dp[nmax+1];

int main(void){
	dp[0]=0.0;
	dp[1]=1.0;
	for(int i=2;i<=nmax;++i){
		double p=1.0,win=0.5;
		for(int k=1;k<i&&eps<p;++k){
			double cur=p*(1.0-win);
			dp[i]+=cur*(k+dp[max(0,i-1-k)]);
			p*=win,win/=2.0;
		}
		dp[i]+=i*p;
	}

	int n;
	cout.precision(3);
	while(cin >> n){
		if(n==0) break;
 		cout << fixed << dp[n] << endl;
	}
	return 0;
}