import java.util.*;

public class Euler339 {

    public static String solve() {
        int n = 10000;
        int max_sum = 2 * n;

        double[] prev = new double[1];
        prev[0] = 0.0;

        for (int s = 1; s <= max_sum; s++) {
            double[] cur = new double[s + 1];
            cur[0] = (double) s;
            cur[s] = 0.0;

            if (s >= 2) {
                int t = (s - 1) / 2;

                for (int w = t + 1; w < s; w++) {
                    cur[w] = prev[w - 1];
                }

                if (t >= 1) {
                    double sLd = (double) s;
                    double rightBoundary = prev[t];

                    double[] b = new double[t + 1];
                    double[] c = new double[t + 1];
                    double[] d = new double[t + 1];

                    b[1] = 1.0;
                    c[1] = (t >= 2) ? (-1.0 / sLd) : 0.0;
                    d[1] = sLd - 1.0;
                    if (t == 1) {
                        d[1] += rightBoundary / sLd;
                    }

                    for (int w = 2; w <= t; w++) {
                        double a = -(double) (s - w) / sLd;
                        double bw = 1.0;
                        double cw = (w < t) ? (-(double) w / sLd) : 0.0;
                        double dw = 0.0;
                        if (w == t) {
                            dw += (double) w * rightBoundary / sLd;
                        }

                        double mult = a / b[w - 1];
                        bw -= mult * c[w - 1];
                        dw -= mult * d[w - 1];

                        b[w] = bw;
                        c[w] = cw;
                        d[w] = dw;
                    }

                    cur[t] = d[t] / b[t];
                    for (int w = t - 1; w >= 1; w--) {
                        cur[w] = (d[w] - c[w] * cur[w + 1]) / b[w];
                    }
                }
            }
            prev = cur;
        }

        double left = prev[n - 1];
        double right = prev[n + 1];
        double ans = 0.5 * (left + right);

        return String.format(Locale.US, "%.6f", ans);
    }

    public static void main(String[] args) {
        System.out.println(solve());
    }
}