Evaluate an Alternating Power Series 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:
$$ S_n = \sum_{i=1}^{n} \frac{(-1)^{i+1} \cdot x^{2i - 1}}{(2i - 1) + 2i} $$
Each term involves an odd power of x, alternating signs, and a denominator formed by the sum of two consecutive integers.

Python Code:

def alternating_series(x, n):
    total = 0
    for i in range(1, n + 1):
        power = 2 * i - 1
        denominator = power + (power + 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 = alternating_series(x, n)
print(f"Result of the series: {result}")

Sample Output:

Enter x: 2  
Enter number of terms n: 4  

Result of the series: -0.190476

Step-by-Step Explanation:

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