Program in python 3.x. Please add comments in order to increase understanding of

Question

Program in python 3.x. Please add comments in order to increase understanding of the solution. (If possible try to make the code as simple as possible). Thanks

Binomial Coefficient Write a function that takes the such as (z +1)n as input, and prints a list of the the coefficients of all polynomials starting with n = 0, using the binomial coefficient. The binomial coefficient is defined as power n of a polynomial n! k) k!(n -k)! For example, if n 3, (x + 1)3-1 + 3x + 3x2 + 2.3. Notice that the coefficients are [1, 3, 3, 1]. You can calculate the coefficients of (x+1)n for n 3 by using the binomial coeff ficient as follows 0 Sample output for (z+ 1)5.

Explanation / Answer

The following Python3 code achieves the required task:

# fact(int x) calculates the factorial of x recursively
# return 1 when x = 0 or x = 1
# else return x*factorial(x-1) {because x! = x*(x-1)!}
def fact(x):
if x==0:
    return 1
if x==1:
    return 1
return x*(fact(x-1))

# nCk(intn, int k) returns the combination value of (n,k)
# calculated as n!/((n-k)!k!)
# Uses the fact() function to calculate factorials
def nCk(n,k):
return int(fact(n)/(fact(n-k)*fact(k)))

# binCoeff(int n) calculates the coefficients in binomial expansion
# of (1+x)^n. Each coeffient is calculated by given formula :
# n!/((n-k)!k!
# Returns the list of coefficients
def binCoeff(n):
coefficients = []                 # Initialize empty list of coefficients
# Iterate from 0 to n (range(a,b) function takes values from i = a to i = b-1, so n+1)
for i in range(0, n+1):       
    coefficients.append(nCk(n,i))   # Append new coefficient to list
return coefficients               # Return the formed list

# The main function begins here
n = int(input("Enter the power 'n' of polynomial (1+x) :")) # Ask for user input
for i in range(0,n+1):
print("(1+x)^"+str(i)+" --> "+str(binCoeff(i)))           # Print output for each i from 0 to n.

Few important notes:

1. After asking for value of n from user, program iterates from i=0 to i=n (inclusive of n, 0) and prints coefficients for (1+x)^i. In code you see i range from 0 to n+1 because range() function takes gives list of values from first number to last number - 1, so range(0, n+1) gives values 0 to (n+1-1) = 0 to n.

2. You can read more about recursive functions (used to calculate factorial here) if you are not familiar, but you can als calculate factorial the traditional way (fact = 1; fact = fact*i where i goes from 1 to n) but this is more efficient.

I have tried to comment anything which can raise doubts.

Hope this helps.

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