Solve in Python:
n passengers board an airplane with exactly n seats. The first passenger has lost the ticket and picks a seat randomly. But after that, the rest of passengers will:

Take their own seat if it is still available, 
Pick other seats randomly when they find their seat occupied 

What is the probability that the n-th person can get his own seat?
 
Example 1:
Input: n = 1
Output: 1.00000
Explanation: The first person can only get the first seat.
Example 2:
Input: n = 2
Output: 0.50000
Explanation: The second person has a probability of 0.5 to get the second seat (when first person gets the first seat).

 
Constraints:

1 <= n <= 10^5
class Solution:
    def nthPersonGetsNthSeat(self, n: int) -> float:
        # if n == 1:
        #     return 1.0
        # else:
        #     return 0.5
        
        if n == 1:
            return 1.0
        sum_results = 0.0
        for i in range(2, n+1):
            p = 1/i * (1 + sum_results)
            sum_results += p
        return p