def even_fibonacci_mathematical(upper_limit):
n = int(round(log(upper_limit * sqrt(5)) / log(PSI)))
last_even_n = n
if fibonacci(n) % 2 != 0:
last_even_n = n - 1
if fibonacci(n - 1) % 2 != 0:
last_even_n = n - 2
return sum_of_nth_first_fibonnaci_numbers(last_even_n) / 2
def sum_of_nth_first_fibonnaci_numbers(last_even_n):
return fibonacci(last_even_n + 2) - 1