Question

The Euler's number can also be calculated using the formula e=∑n=0[infinity]​n!1​=1+1!1​+2!1​+3!1​+⋯ Please program this formula using Python. A cut-off n should be a few hundred. Hint: This program may need imbedded for loops. Also, you need to take care of the calculation issue of factorials with large n, i.e., 1/(n+1)!=(1/n!)×[1/(n+1)].

Answer 1

To program the calculation of Euler's number using the given formula, you can use a nested for loop structure in Python.

Step-by-step explanation:

To program the calculation of Euler's number using the given formula, you can use a nested for loop structure in Python. Here's an example code:

def calculate_euler(n):
result = 1
factorial = 1
for i in range(1, n+1):
factorial *= i
result += 1/factorial
return result

# Testing the function
print(calculate_euler(100))

By setting the value of 'n' to the desired cutoff, you can calculate the Euler's number approximation. The function calculates the factorial of 'n' using the nested for loop and adds the reciprocal of the factorial to the result. It then returns the final approximate value of Euler's number.