Program to Compute the Value of Euler’s Number ,Using the Formula e = 1 + 11! + 12! + …… 1n!

Eulers number excel – Python Program to Compute the Value of Euler’s Number ,Using the Formula: e = 1 + 1/1! + 1/2! + …… 1/n!

by

Euler’s number python: Our website provided core java programs examples with output aid beginners and expert coders to test their knowledge gap and learn accordingly.

Refer these:

  • Python program to compute the value of eulers number e use the formula e 1 1 1 12 1n.
  • Python program to compute sum of 1 x2 x23 xnn1.
  • 1122 33 python.
  • 1/1/2/2 3/3 python.

Given a number numb, the task is to compute the value of the Euler’s number expansion in Python.

Examples:

Example1:

Input:

given number =3

Output:

Enter some random number = 3
The total sum of euler's value of the series 2.67

Example2:

Input:

given number =5

Output:

The total sum of euler's value of the series  2.72

Program to Compute the Value of Euler’s Number ,Using the Formula: e = 1 + 1/1! + 1/2! + …… 1/n! in Python

Eulers number excel: There are several ways to calculate the value of the euler’s number some of them are:

Method #1:Using factorial function and for loop(Static Input)

Approach:

  • Give the number as static input.
  • Set the value of the totalsum variable to 1.
  • Find the total of the series using a for loop ranging from 1 to the number.
  • Compute the factorial using math. factorial() function.
  • After rounding to two decimal places, print the totalsum of the series.
  • Exit of program.

Below is the implementation:

import math
# Give the number of terms as static input.
numb = 5
# Set a totalsum variable which calculates the total sum and initialize it to 1.
totalsum = 1
# Find the total of the series using a for loop ranging from 1 to the number.
for val in range(1, numb+1):
  # Compute the factorial using math. factorial() function.
    totalsum = totalsum+(1/math.factorial(val))
# Print the totalsum value of the euler's series, rounded to two decimal places.
print("The total sum of euler's value of the series ", round(totalsum, 2))

Output:

The total sum of euler's value of the series  2.72

Method #2:Using factorial function and for loop(User Input)

Approach:

  • Scan the given number as user input by using int(input()) function.
  • Set the value of the totalsum variable to 1.
  • Find the total of the series using a for loop ranging from 1 to the number.
  • Compute the factorial using math. factorial() function.
  • After rounding to two decimal places, print the totalsum of the series.
  • Exit of program.

Below is the implementation:

import math
#  Scan the number as user input by using int(input()) function
numb = int(input('Enter some random number = '))
# Set a totalsum variable which calculates the total sum and initialize it to 1.
totalsum = 1
# Find the total of the series using a for loop ranging from 1 to the number.
for val in range(1, numb+1):
  # Compute the factorial using math. factorial() function.
    totalsum = totalsum+(1/math.factorial(val))
# Print the totalsum value of the euler's series, rounded to two decimal places.
print("The total sum of euler's value of the series ", round(totalsum, 2))

Output:

Enter some random number = 13
The total sum of euler's value of the series 2.72

Method #3:Using factorial function and while loop(Static Input)

Approach:

  • Give the number as static input.
  • Set a totalsum variable which calculates the total sum and initialize it to 0.
  • Take a variable say value and initialize it to 1.
  • Using while loop calculate the total sum till value greater than given number
  • Compute the factorial using math. factorial() function.
  • Calculate the totalsum by incrementing it value with 1/factorial value.
  • Increment the value by 1.
  • Print the totalsum of the series, rounded to two decimal places.
  • Exit of program.

Below is the implementation:

import math
# Give the number of terms as static input.
numb = 3
# Take a variable say value and initialize it to 1.
value = 1
# Set a totalsum variable which calculates the total sum and initialize it to 1.
totalsum = 1
# Using while loop calculate the total sum till value greater than given number
while(value <= numb):
   # Compute the factorial using math. factorial() function.
    totalsum = totalsum+(1/math.factorial(value))
    # Increment the value by 1.
    value = value+1
# Print the totalsum value of the euler's series, rounded to two decimal places.
print("The total sum of euler's value of the series ", round(totalsum, 2))

Output:

The total sum of euler's value of the series 2.67

Method #4:Using factorial function and while loop(User Input)

Approach:

  • Scan the given number as user input by using int(input()) function.
  • Set a totalsum variable which calculates the total sum and initialize it to 0.
  • Take a variable say value and initialize it to 1.
  • Using while loop calculate the total sum till value greater than given number
  • Compute the factorial using math. factorial() function.
  • Calculate the totalsum by incrementing it value with 1/factorial value.
  • Increment the value by 1.
  • Print the totalsum of the series, rounded to two decimal places.
  • Exit of program.

Below is the implementation:

import math
# Scan the number as user input by using int(input()) function
numb = int(input('Enter some random number = '))
# Take a variable say value and initialize it to 1.
value = 1
# Set a totalsum variable which calculates the total sum and initialize it to 1.
totalsum = 1
# Using while loop calculate the total sum till value greater than given number
while(value <= numb):
   # Compute the factorial using math. factorial() function.
    totalsum = totalsum+(1/math.factorial(value))
    # Increment the value by 1.
    value = value+1
# Print the totalsum value of the euler's series, rounded to two decimal places.
print("The total sum of euler's value of the series ", round(totalsum, 2))

Output:

Enter some random number = 3
The total sum of euler's value of the series 2.67

Test yourself:

  1. Write a python program to find the value of e using infinite series of the function?
  2. Write a program to compute 122334 nn1 in python?
  3. Write ac program to compute the value of eulers number e use the formula e 11 1 12 13 1n?
  4. Write a program to compute 1/2/2/3+3/4 n/n+1 in python?
  5. Write ac program to compute the value of euler’s number e use the formula e 1/1 + 1 + 1/2 1/3 1/n?
  6. Python program to find sum of series 1 + x + x^2?
  7. Python program to compute the value of euler’s number e use the formula e = 1 + 1 + 1 + 1/2 1/n?
  8. Python program to find sum of the series 1/1/1/2 + 1/3 + 1/n?
  9. Python program to find sum of the series 1112 13 1n?
  10. Python program to find sum of series 1 x x2?

Related Programs: