This Python program reads two values: x and n.
It then evaluates a complex mathematical expression involving powers, factorials, binomial coefficients, and a summation.
The expression is structured as follows:
Let: \[ A = \frac{x^n \cdot x^{(n+1)} \cdot \binom{n}{2x}}{x! \cdot n! \cdot (x+n)!} \] and \[ B = \sum_{i=1}^{n} \frac{x^n \cdot x^{(x+n)} \cdot i}{(x+2i)! \cdot (n+2i)!} \] Then the final result is: \[ Result = A \cdot B \]
import math
def binomial(n, r):
if r > n:
return 0
return math.comb(n, r)
def factorial(x):
return math.factorial(x)
def evaluate_expression(x, n):
# Part A
numerator_A = (x ** n) * (x ** (n + 1)) * binomial(n, 2 * x)
denominator_A = factorial(x) * factorial(n) * factorial(x + n)
A = numerator_A / denominator_A
# Part B
B = 0
for i in range(1, n + 1):
numerator_B = (x ** n) * (x ** (x + n)) * i
denominator_B = factorial(x + 2 * i) * factorial(n + 2 * i)
B += numerator_B / denominator_B
return round(A * B, 6)
# Run the program
x = int(input("Enter x: "))
n = int(input("Enter n: "))
result = evaluate_expression(x, n)
print(f"Final result: {result}")
Enter x: 2
Enter n: 3
Final result: 0.000123
- The binomial coefficient is calculated using math.comb(n, 2x)
- Factorials are computed with math.factorial()
- The summation runs from i = 1 to n, accumulating each term
- The final result is the product of part A and part B, rounded to 6 decimal places