Python Math: Compute the value of e using infinite series

Last update on April 02 2025 12:29:22 (UTC/GMT +8 hours)

65. Euler's Number (e) Approximation

Write a Python program to compute the value of e(2.718281827...) using an infinite series.

Sample Solution:

Python Code:

''' 
#https://gist.github.com/thinkphp/1528363

  1 + 1/1! + 1/2! + 1/3! + ...
  2 + 1/2! + 1/3!+ ...
'''
import math

def fact(n):
    if n == 0:
       return 1
    else:
       return n*fact(n-1)

def e(EPS):

    v1 = 2
    v2 = v1 + float(1.0/fact(2))
    i = 3 
    while math.fabs(v1-v2) >= EPS:
          v1 = v2
          v2 += float(1.0/fact(i))
          i += 1
    return v2  

print("The mathematical constant e")
#computes the value of e using infinite series
print(e(0.00000001))
#mathematical constant e build-in
print(math.e)

Sample Output:

The mathematical constant e                                                                                   
2.7182818282861687                                                                                            
2.718281828459045

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to approximate Euler's number e using an infinite series, summing terms until the change is less than a specified tolerance.
• Write a Python function that computes e using a recursive approach and returns the approximate value after n iterations.
• Write a Python script to compare your computed value of e with math.e and print the absolute difference.
• Write a Python program to display a convergence table showing the approximate value of e with an increasing number of terms.

Python Code Editor:

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