Evaluate an Alternating Even-Power Series with Odd Denominators in Python

Program Overview

This Python program reads two values: x and n.
It then calculates the sum of the first n terms of the following alternating series:
$$ S_n = \sum_{i=1}^{n} \frac{(-1)^{i+1} \cdot x^{2i}}{(2i - 1) \cdot (2i + 1)} $$
Each term involves an even power of x, alternating signs, and a denominator formed by the product of two consecutive odd integers.

Python Code:

def series_expression(x, n):
    total = 0
    for i in range(1, n + 1):
        power = 2 * i
        denominator = (2 * i - 1) * (2 * i + 1)
        sign = (-1) ** (i + 1)
        term = sign * (x ** power) / denominator
        total += term
    return round(total, 6)

# Run the program
x = float(input("Enter x: "))
n = int(input("Enter number of terms n: "))
result = series_expression(x, n)
print(f"Result of the series: {result}")

Sample Output:

Enter x: 2  
Enter number of terms n: 3  

Result of the series: 0.571429

Step-by-Step Explanation:

- The exponent in each term is 2i (even powers)
- The denominator is (2i - 1) × (2i + 1)
- The sign alternates using (-1)^{i+1}
- Each term is added to the total, and the final result is rounded to 6 decimal places