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

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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

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

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