Evaluate a Custom Alternating Series with Powers of x 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:
$$ S_n = \sum_{i=1}^{n} \frac{(-1)^{i+1} \cdot (2^i \cdot x^i)}{i + 2^i} $$
Each term includes a power of x multiplied by 2^i, divided by the sum i + 2^i, and alternates in sign.

Python Code:

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

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

Sample Output:

Enter x: 2  
Enter number of terms n: 3  

Result of the series: 2.133333

Step-by-Step Explanation:

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