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.