Python Math: Compute the value of e using infinite series

Last update on August 11 2025 12:35:31 (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 mathdef 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 seriesprint(e(0.00000001))#mathematical constant e build-inprint(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.

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