13. Program to calculate for BINOMIAL SERIES and MID TERM

#Program to calculate binomial series and middle term

import math

check=int(input(''' Please choose

1. For middle term

2. For binomial theorem'''))

#This is for finding the factorial for combination

def factorial(number):

    c=1

    if(number==0):

        return 1

    for i in range(number,0,-1):

        c=c*i

    return c

def combination(p,q):

    if(p>=q):

        

        return factorial(p)/(factorial(q)*factorial(p-q))

    else:

        print('you have written n less which is incorrect')

def midtermfind(limit,termid):

    print('Program to find the answer by binomial series ')

    print('series is in the sequence (a+b) to the power n')

    a=int(input('enter a of the formula'))

    b=int(input('enter b of the formula'))

    result=0

    

    comb=combination(int(limit),int(termid))

    result=result+(comb*math.pow(a,(limit-termid))*math.pow(b,termid))

    print('The mid term  is =',int(result))

    

def binomial():

    print('Program to find the answer by binomial series ')

    print('series is in the sequence (a+b) to the power n')

    a=int(input('enter a of the formula'))

    b=int(input('enter b of the formula'))

    n=int(input('enter n of the formula'))

    result=0

    

    for i in range(0,n+1):

        comb=combination(n,i)

        result=result+(comb*math.pow(a,(n-i))*math.pow(b,i))

    print('The result for this is =',int(result))

def midterm():

    n=int(input('enter the power n of the series '))

    if(n%2==0):

        print(n,'is even number and it has only one mid term')

        mid=(n/2+1)

        print('The mid term is',int(mid),'term')

        midcheck=1

    elif(n%2!=0):

        print(n,'is odd number and it has 2 mid term')

        mid=(n+1)/2

        mid2=(n+3)/2

        print('First middle term is',int(mid),'term  and second mid term is',int(mid2),'term')

        midcheck=1

    while(midcheck==1):

        midchoice=int(input('press 1 if you want to know the middle term'))

        if(midchoice==1):

            midtermfind(n,mid)

            midcheck=0

        else:

            print('you have entered wrong key ')

        

#to check the choice 

if(check==1):

    midterm()

if(check==2):

    binomial()