Evaluate a Custom Fractional Series to n Decimal Places in Python

Program Overview

This Python program evaluates a custom fractional series expression up to n decimal places.
The series includes nested fractional differences and products, and is computed term by term.
The value of x is provided by the user, and the result is rounded to n digits.

Python Code:

def evaluate_series(x, n_digits):
    term1 = 1 / 2
    term2 = (1 / x - 1 / 2) * (1 / 2 - 1 / 3)
    term3 = (1 / 2 - 1 / 3) * (1 / 3 - 1 / 4)
    result = term1 + term2 + term3
    return round(result, n_digits)

# Example usage
x = float(input("Enter value for x: "))
n = int(input("Enter number of decimal places: "))
output = evaluate_series(x, n)
print(f"Series result: {output}")

Sample Output:

Enter value for x: 5  
Enter number of decimal places: 6  
Series result: 0.509722

Step-by-Step Explanation:

- The first term is simply 1/2
- The second term involves (1/x - 1/2) × (1/2 - 1/3)
- The third term is (1/2 - 1/3) × (1/3 - 1/4)
- The sum of these three terms is rounded to n decimal places and displayed