Calculate General Term in Java (Binomial Theorem)

This illustrates calculating the general term in a bionomial expansion (x+a)^n using the standard bionomial theorem formula for calculating the general term.

The forumla used is ((nCr)*(x^(n-r))*(a^r))

import java.util.*;

class GeneralTerm

{

    public static void main(String args[])

    {

    

    // Create Scanner object

    Scanner s=new Scanner(System.in);



    

    System.out.println("Enter the values of x,a,n in (x+a)^n");



    // Take values of x,a,n respectively

    int x=s.nextInt();

    int a=s.nextInt();

    int n=s.nextInt();



    System.out.println("Enter the value of r to find general term");



    // Take the value of r

    int r=s.nextInt();





    // To calculate nCr   

    long nCr=calculatenCr(n,r);



       

        // nCr is -1 when n<r

        if(nCr!=-1)

        {

            // Calculate x^(n-r)

            double y=Math.pow((double)x,(double)n-r);



            // Calculate a^r

            double z=Math.pow((double)a,(double)r);



            // Calculate and Print general term ((nCr)*(x^(n-r))*(a^r))

            System.out.println("The result is "+nCr*y*z);

        }       

    

    }





    // Method to calculate nCr

    public static long calculatenCr(int n,int r)

    {



    long res=1;



        if(n>=r)

        {

            res=getFact(n)/(getFact(n-r)*getFact(r));

            return res;

        }

        else return -1;



    }



    public static long getFact(int n)

    {

        long f=1;



        for(int i=n;i>=1;i--)

        {

        f*=i;

        }



    return f;

    }



}

Sample Output

Enter the values of x,a,n in (x+a)^n

5

4

2

Enter the value of r to find general term

2

The result is 16.0

Analysis

nCr=-1: -1 is returned if n<r which is absurd.

nCr!=-1: If n>r then nCr is not equal to -1.

Math.pow((double)x,(double)n-r): This (pow) is a method of java.lang.Math class which takes two double values and find the power. The first parameter is the number and the second one is the power. As x and n-r are long values, they are typecasted into double. This method returns a double value which is the required result. Therefore, x^(n-r) [x to the power n-r] is calculated. Similarily, a^r (a power r) is also calculated.

The General Term:  The general term formula is ((nCr)*(x^(n-r))*(a^r)). The general term is also called as rth term.

Calculating combination: This is discussed in finding number of combinations in Java
Factorial: This is discussed in finding factorial of a number in Java post.

In this way we can calculate the general term in binomial theorem in Java.