[Solved] show function approaches certain value

riven Asks: show function approaches certain value
the following is my code for to solve this question :

Show that as n increases (e.g. with a doubling experiment), from n = 2 to n = 1,000, the value of “day_sim(n)” approaches “sqrt(pi * n / 2)”.

I have set the “day_sim(n)” function, but don’t know how to start the quoted question of “show that is approaches “sqrt(pi * n / 2)”

Please help me with cracking this

Code:
import random
from random import randint 
import numpy as np

def randomgen(n):
    np.random.randint(low = 0, high = n)
    return random.randint(0,n-1)

randomgen(100)

def day(n):
    result = []
    random = randomgen(n)
    count =0
    while random not in result:
        result.append(random)
        random = randomgen(n)
        count += 1
    return count
day(100)
    

def day_sim(n):
    n_trials = 10000
    day_sim = [birthday(n) for _ in range(n_trials)]
    return day_sim
 
day_sim(N)

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