Every Day is a Holiday
Problem 645
On planet J, a year lasts for days. Holidays are defined by the two following rules.
Initially there are no holidays. Let be the expected number of Emperors to reign before all the days of the year are holidays, assuming that their birthdays are independent and uniformly distributed throughout the days of the year.
You are given , , .
Find . Give your answer rounded to 4 digits after the decimal point.