// template {{{

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

#define loop(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rep(i, n) loop(i, 0, n)
#define rloop(i, a, b) for (int i = (int)(b) - 1; i >= (int)(a); i--)
#define rrep(i, n) rloop(i, 0, n)
#define eb emplace_back
#define ef emplace_front
#define pb pop_back
#define pf pop_front
#define all(c) std::begin(c), std::end(c)
#define mp std::make_pair
#define mt std::make_tuple
#define fi first
#define se second
#define popcnt __builtin_popcountll

using uint = unsigned;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vd = vector<double>;
using vvd = vector<vd>;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<double, double>;
using tp = tuple<int, int, int>;
using tp4 = tuple<int, int, int, int>;
using tp5 = tuple<int, int, int, int, int>;

template<typename T>
using max_pq = priority_queue<T, vector<T>, less<T>>;

template<typename T>
using min_pq = priority_queue<T, vector<T>, greater<T>>;

const int MOD = 1e9 + 7;
const int INF = 1e9 + 10;
const ll LLINF = 1e18 + 10;

const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, -1, 0, 1};
const int dx8[] = {-1, -1, 0, 1, 1, 1, 0, -1};
const int dy8[] = {0, -1, -1, -1, 0, 1, 1, 1};

template<typename T>
inline T sq(T x){ return x * x; }

template<typename T, typename U>
inline bool chmax(T &x, U y){ if (x >= y) return false; x = y; return true; }

template<typename T, typename U>
inline bool chmin(T &x, U y){ if (x <= y) return false; x = y; return true; }

template<typename T>
inline void sort(T &c){ std::sort(std::begin(c), std::end(c)); }

template<typename T>
inline void reverse(T &c){ std::reverse(std::begin(c), std::end(c)); }

template<typename T>
inline void unique(T &c){ std::sort(std::begin(c), std::end(c)); c.erase(std::unique(all(c)), std::end(c)); }

// }}}

int n;
double dp[100010][30];
double p[30];

double calc(int i, int j)
{
	if (i == 0 || j >= 30) return 0.0;
	if (dp[i][j] != -1.0) return dp[i][j];
	return dp[i][j] = p[j] * (1 + calc(i - 1, j + 1)) + (1 - p[j]) * calc(i - 1, 0);
}

int main()
{
	fill_n(*dp, 100010 * 30, -1.0);
	p[0] = 1.0;
	rep(i, 29) p[i + 1] = p[i] / 2;
	while (cin >> n, n){
		printf("%.20lf\n", calc(n, 0));
	}
}