using System;
using System.Collections.Generic;
using System.Linq;

class Solver
{
    void Solve()
    {
        //dp[i,j] ith day, get bentoh j straight days.
        var dp = new double[100050, 50];
        var E = new double[100050];
        var p = new double[50];
        p[0] = dp[0, 0] = 1.0;
        for (int i = 1; i < 50; i++)
            p[i] = p[i - 1] / 2;
        for (int i = 0; i <= 100000; i++)
        {

            for (int j = 0; j < 15; j++)
            {
                if (dp[i, j] <= 0)
                    continue;
                dp[i + 1, 0] += dp[i, j] * (1 - p[j]);
                dp[i + 1, j + 1] += dp[i, j] * p[j];
                E[i + 1] += dp[i, j] * p[j];
            }
            E[i + 1] += E[i];
        }
        while (true)
        {
            var n = sc.Integer();
            if (n == 0)
                return;
            Printer.PrintLine("{0:F12}",E[n]);

        }


    }
    static void Main()
    {
#if DEBUG
        var oStream = new System.IO.FileStream("debug.txt", System.IO.FileMode.Create, System.IO.FileAccess.Write);
        var iStream = new System.IO.FileStream("input.txt", System.IO.FileMode.Open, System.IO.FileAccess.Read, System.IO.FileShare.ReadWrite);
        Console.SetIn(new System.IO.StreamReader(iStream));
        System.Diagnostics.Debug.AutoFlush = true;
        System.Diagnostics.Debug.Listeners.Add(new System.Diagnostics.TextWriterTraceListener(new System.IO.StreamWriter(oStream, System.Text.Encoding.UTF8)));
        try
        {
#endif
            var solver = new Solver();
            solver.Solve();
#if DEBUG
        }
        catch (Exception ex)
        {
            Console.WriteLine(ex.Message);
            Console.WriteLine(ex.StackTrace);
        }
        Console.ReadKey(true);
#endif
    }
    _Scanner sc = new _Scanner(Console.In);

}
static public class Printer
{
    static readonly private System.IO.TextWriter writer;
    static readonly private System.Globalization.CultureInfo info;
    static string Separator { get; set; }
    static Printer()
    {
        writer = Console.Out;
        info = System.Globalization.CultureInfo.InvariantCulture;
        Separator = " ";
    }

    static public void Print(int num) { writer.Write(num.ToString(info)); }
    static public void Print(int num, string format) { writer.Write(num.ToString(format, info)); }
    static public void Print(long num) { writer.Write(num.ToString(info)); }
    static public void Print(long num, string format) { writer.Write(num.ToString(format, info)); }
    static public void Print(double num) { writer.Write(num.ToString(info)); }
    static public void Print(double num, string format) { writer.Write(num.ToString(format, info)); }
    static public void Print(string str) { writer.Write(str); }
    static public void Print(string format, params object[] arg) { writer.Write(format, arg); }
    static public void Print(IEnumerable<char> sources) { writer.Write(sources.AsString()); }
    static public void Print(params object[] arg)
    {
        var res = new System.Text.StringBuilder();
        foreach (var x in arg)
        {
            res.AppendFormat(info, "{0}", x);
            if (!string.IsNullOrEmpty(Separator))
                res.Append(Separator);
        }
        writer.Write(res.ToString(0, res.Length - Separator.Length));
    }
    static public void Print<T>(IEnumerable<T> sources)
    {
        var res = new System.Text.StringBuilder();
        foreach (var x in sources)
        {
            res.AppendFormat(info, "{0}", x);
            if (string.IsNullOrEmpty(Separator))
                res.Append(Separator);
        }
        writer.Write(res.ToString(0, res.Length - Separator.Length));
    }
    static public void PrintLine(int num) { writer.WriteLine(num.ToString(info)); }
    static public void PrintLine(int num, string format) { writer.WriteLine(num.ToString(format, info)); }
    static public void PrintLine(long num) { writer.WriteLine(num.ToString(info)); }
    static public void PrintLine(long num, string format) { writer.WriteLine(num.ToString(format, info)); }
    static public void PrintLine(double num) { writer.WriteLine(num.ToString(info)); }
    static public void PrintLine(double num, string format) { writer.WriteLine(num.ToString(format, info)); }
    static public void PrintLine(string str) { writer.WriteLine(str); }
    static public void PrintLine(string format, params object[] arg) { writer.WriteLine(format, arg); }
    static public void PrintLine(IEnumerable<char> sources) { writer.WriteLine(sources.AsString()); }
    static public void PrintLine(params object[] arg)
    {
        var res = new System.Text.StringBuilder();
        foreach (var x in arg)
        {
            res.AppendFormat(info, "{0}", x);
            if (!string.IsNullOrEmpty(Separator))
                res.Append(Separator);
        }
        writer.WriteLine(res.ToString(0, res.Length - Separator.Length));
    }
    static public void PrintLine<T>(IEnumerable<T> sources)
    {
        var res = new System.Text.StringBuilder();
        foreach (var x in sources)
        {
            res.AppendFormat(info, "{0}", x);
            if (!string.IsNullOrEmpty(Separator))
                res.Append(Separator);
        }
        writer.WriteLine(res.ToString(0, res.Length - Separator.Length));
    }
}
public class _Scanner
{
    readonly private System.Globalization.CultureInfo info;
    readonly System.IO.TextReader reader;
    string[] buffer = new string[0];
    int position;

    public char[] Separator { get; set; }
    public _Scanner(System.IO.TextReader reader, string separator = null, System.Globalization.CultureInfo info = null)
    {
        if (reader == null)
            throw new ArgumentNullException("reader");
        this.reader = reader;
        if (string.IsNullOrEmpty(separator))
            separator = " ";
        this.Separator = separator.ToCharArray();
        this.info = info ?? System.Globalization.CultureInfo.InvariantCulture;
    }
    public string Scan()
    {
        if (this.position < this.buffer.Length)
            return this.buffer[this.position++];
        this.buffer = this.reader.ReadLine().Split(this.Separator, StringSplitOptions.RemoveEmptyEntries);
        this.position = 0;
        return this.buffer[this.position++];
    }

    public string[] ScanToEndLine()
    {
        if (this.position >= this.buffer.Length)
            return this.reader.ReadLine().Split(this.Separator, StringSplitOptions.RemoveEmptyEntries);
        var size = this.buffer.Length - this.position;
        var ar = new string[size];
        Array.Copy(this.buffer, position, ar, 0, size);
        return ar;

    }

    public string ScanLine()
    {
        if (this.position >= this.buffer.Length)
            return this.reader.ReadLine();
        else
        {
            var sb = new System.Text.StringBuilder();
            for (; this.position < buffer.Length; this.position++)
            {
                sb.Append(this.buffer[this.position]);
                sb.Append(' ');
            }
            return sb.ToString();
        }
    }
    public string[] ScanArray(int length)
    {
        var ar = new string[length];
        for (int i = 0; i < length; i++)
        {
            ar[i] = this.Scan();
        }
        return ar;
    }

    public int Integer()
    {
        return int.Parse(this.Scan(), info);
    }
    public long Long()
    {
        return long.Parse(this.Scan(), info);
    }
    public double Double()
    {
        return double.Parse(this.Scan(), info);
    }
    public double Double(string str)
    {
        return double.Parse(str, info);
    }

    public int[] IntArray(int length)
    {
        var a = new int[length];
        for (int i = 0; i < length; i++)
            a[i] = this.Integer();
        return a;
    }
    public long[] LongArray(int length)
    {
        var a = new long[length];
        for (int i = 0; i < length; i++)
            a[i] = this.Long();
        return a;
    }
    public double[] DoubleArray(int length)
    {
        var a = new double[length];
        for (int i = 0; i < length; i++)
            a[i] = this.Double();
        return a;
    }

}
static public partial class EnumerableEx
{
    static public string AsString(this IEnumerable<char> source)
    {
        return new string(source.ToArray());
    }
    static public T[] EnumerateArray<T>(this int count, Func<int, T> selector)
    {
        var ret = new T[count];
        for (int i = 0; i < count; i++)
            ret[i] = selector(i);
        return ret;
    }
}

//*/


Measured memory_bytes: 46332