Several example codes

Program Overview

This Python program reads two values x and n and computes the result of the following series:
1 + ∑ [(n(n-1)...(n-k+1) · x^k) / k!] for k from 1 to n
It uses a helper function to compute the descending product and standard factorial for the denominator.

Python Code:

import math

def descending_product(n: int, k: int) -> int:
    result = 1
    for i in range(k):
        result *= (n - i)
    return result

def compute_series(x: float, n: int) -> float:
    total = 1.0
    for k in range(1, n + 1):
        numerator = descending_product(n, k) * (x ** k)
        denominator = math.factorial(k)
        total += numerator / denominator
    return total

# Read inputs from user
x = float(input("Enter value for x: "))
n = int(input("Enter value for n: "))

result = compute_series(x, n)
print(f"Series result is: {result:.6f}")

Sample Output (input: x = 2, n = 3):

Series result is: 21.000000