#include<iostream>
#include<iomanip>
#include<algorithm>
#include<array>
#include<bitset>
#include<cassert>
#include<cctype>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<functional>
#include<limits>
#include<list>
#include<map>
#include<numeric>
#include<set>
#include<stack>
#include<string>
#include<sstream>
#include<unordered_map>
#include<queue>
#include<vector>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;

#define rep(i,p,b) for(int i=(p);i<(b);i++)
#define rrep(i,p,b) for(int i=(b)-1;i>=(p);i--)
#define all(p) (p).begin(),(p).end()
#define dump(o) {cerr<<#o<<" "<<o<<endl;}
#define dumpc(o) {cerr<<#o; for(auto &e:(o))cerr<<" "<<e;cerr<<endl;}
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
const int MOD = 1e9 + 7;

#define MAX 100010
#define B 15

signed main() {
	cout << fixed << setprecision(8);
	static double dp[MAX][B] = {}; dp[1][1] = 1;
	static double p[B] = {};
	static double ans[MAX] = {};
	double sum = 0;
	rep(i, 1, B)p[i] = pow(0.5, i - 1);
	rep(i, 1, MAX - 1) {
		rep(j, 1, B) {
			if (dp[i][j] == 0)continue;
			sum += dp[i][j] * p[j];
			dp[i + 1][1] += dp[i][j] * (1 - p[j]);
			dp[i + 1][j + 1] += dp[i][j] * p[j];
		}
		ans[i] = sum;
	}
	for (int n; cin >> n&&n;) {
		cout << ans[n] << endl;
	}
	return 0;
}