Day 54: Python Program to Find Sum of Series 1/1!+1/2!+1/3!....1/N!

import math

def sum_of_series(n):

    """

    Calculates the sum of the series 1/1! + 1/2! + 1/3! + ... + 1/N!

    :param n: The number of terms in the series

    :return: The sum of the series

    """

    if n <= 0:

        return "N should be a positive integer."

    

    total_sum = 0

    for i in range(1, n + 1):

        total_sum += 1 / math.factorial(i)  

    return total_sum

try:

    N = int(input("Enter a positive integer N: "))

    if N <= 0:

        print("Please enter a positive integer.")

    else:

        result = sum_of_series(N)

        print(f"The sum of the series for N={N} is: {result:.6f}")

except ValueError:

    print("Invalid input! Please enter a positive integer.")

#source code --> clcoding.com 

Code Explanation:

1. Importing the math module:

import math

The math module provides access to mathematical functions, including math.factorial() used in this program.

2. Function Definition:

def sum_of_series(n):

    """

    Calculates the sum of the series 1/1! + 1/2! + 1/3! + ... + 1/N!

    :param n: The number of terms in the series

    :return: The sum of the series

    """

This function calculates the sum of the series up to 𝑁 terms.

3. Input Validation:

if n <= 0:

    return "N should be a positive integer."

Ensures that N is a positive integer. If  N≤0, an error message is returned.

4. Series Calculation:

total_sum = 0

for i in range(1, n + 1):

    total_sum += 1 / math.factorial(i)

total_sum: Accumulates the sum of the series. Initially set to 0.

for i in range(1, n + 1): Loops through integers from 1 to 𝑁

math.factorial(i): Computes i!, the factorial of 𝑖

1 / math.factorial(i): Adds the term 1/𝑖! to the total sum.

5. Returning the Result:

return total_sum

Returns the computed sum of the series.

6. User Input Handling:

try:

    N = int(input("Enter a positive integer N: "))

    if N <= 0:

        print("Please enter a positive integer.")

    else:

        result = sum_of_series(N)

        print(f"The sum of the series for N={N} is: {result:.6f}")

except ValueError:

    print("Invalid input! Please enter a positive integer.")

try block:

Prompts the user for an integer input for 𝑁.

If the user enters a valid positive integer:

Checks if 

N>0. If not, prints an error message.

Otherwise, calls sum_of_series(N) to compute the sum and prints the result with six decimal places.

except block:

Handles invalid inputs (e.g., entering a string or decimal) and displays an error message.