import math
def calculate_e_formula1(n):
return (1 + 1 / n) ** n
def calculate_e_formula2(n):
e = 0
factorial = 1
for k in range(n + 1):
if k == 0:
factorial = 1
else:
factorial *= k
e += 1 / factorial
return e
n = 1000
e_formula1 = calculate_e_formula1(n)
e_formula2 = calculate_e_formula2(n)
print( e_formula1)
print( e_formula2)
print( math.e)
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