# Java Program to Compute an-bn when n is a Natural Number

In the previous article we have discussed Java Program to Compute 2(ab+bc+ca) where Value of a, b and c are Given

In this program we are going to see how to compute an-bn   where value of a and b are given and when n is a natural number by using Java programming language.

### Java Program to Compute an-bn when n is a Natural Number

The formula of an-bn is given below.

an-bn  = (a−b)(an−1+an−2b+an−3b2+…+abn−2+bn−1)

Example:

Suppose a=4, b=2, and n=3

Then

an-bn  =(a−b)(an−1+an−2b+an−3b2+…+abn−2+bn−1)

=(4-2)*(43-1*23-3 + 43-2*23-2 + 43-3*23-1)

=2*(16+8+4)

=2*28

=56

Now let’s see different ways to compute an-bn

### Method-1: Java Program to Compute an-bn when n is a Natural Number By Using pow() Function and Static Input Value

Approach:

• Declare and initialize two integer variables say a and b.
• Declare another integer variable say n, which is denoted as power value of the formula.
• Take the value of a, b, and n as user input by using Scanner class.
• By using the formula compute an-bn .
• Print the result.

Program:

import java.util.Scanner;
class Main
{
public static void main(String[] args)
{
//Declare the first input from the user.
int a= 10;
System.out.println("a= "+a);
// Declare the second input from the user.
int b= 8;
System.out.println("b= "+b);
// Declare the third input from the user.
int n= 12;
System.out.println("n= "+n);
//declare another integer variable and assigned the  (a-b) value to it.
int c= a-b;
long sum=0;
//Appling for loop for looping the formula.
for(int i=1;i<=n;i++)
{
int e=n-(n-i+1);
double d=Math.pow(a,n-i)*Math.pow(b,e);
sum=sum+(long)d;
}
//print the result
System.out.println("an-bn= "+sum*c);
}
}

Output:

a= 10
b= 8
n= 12
an-bn= 931280523264

### Method-2: Java Program to Compute an-bn when n is a Natural Number By Using pow() Function and User Input Value

Approach:

• Declare and initialize two integer variables say a and b.
• Declare another integer variable say n, which is denoted as power value of the formula.
• Take the value of a, b, and n as user input by using Scanner class.
• By using the formula compute an-bn .
• Print the result.

Program:

import java.lang.Math;
import java.util.Scanner;
class Main{
public static void main(String[] args){
//create object of scanner class.
Scanner sc=new Scanner(System.in);
System.out.print("a= ");
//Take the first input from the user.
int a= sc.nextInt();
System.out.print("b= ");
//Take the second input from the user.
int b= sc.nextInt();
System.out.print("n= ");
//Take the third input from the user.
int n= sc.nextInt();
//declare another integer variable and assigned the  (a-b) value to it.
int c= a-b;
long sum=0;
//Appling for loop for looping the formula.
for(int i=1;i<=n;i++){
int e=n-(n-i+1);
double d=Math.pow(a,n-i)*Math.pow(b,e);
sum=sum+(long)d;
}
//print the result
System.out.println("an-bn= "+sum*c);
}
}

Output:

a= 10
b= 8
n= 12
an-bn= 931280523264

### Method-3: Java Program to Compute an-bn when n is a Natural Number By Using User Defined Method

Approach:

• Declare two integer variables say a and b.
• Declare another integer variable say n, which is denoted as power value of the formula.
• Take the value of a, b, and n as user input by using Scanner class.
• Then call a user defined method say computeValue() and pass a and b as parameter.
• Then inside method by using the formula compute an-bn .
• Print the result.

Program:

import java.util.Scanner;
class Main
{
public static void main(String[] args)
{
//create object of scanner class.
Scanner sc=new Scanner(System.in);
System.out.print("a= ");
//Take the first input from the user.
int a= sc.nextInt();
System.out.print("b= ");
//Take the second input from the user.
int b= sc.nextInt();
System.out.print("n= ");
//Take the third input from the user.
int n= sc.nextInt();
//call the user defined method
computeValue(a,b,n);
}

//define the method
public static void computeValue(int a, int b, int n)
{
//declare another integer variable and assigned the  (a-b) value to it.
int c= a-b;
long sum=0;
//Appling for loop for looping the formula.
for(int i=1;i<=n;i++)
{
int e=n-(n-i+1);
double d=Math.pow(a,n-i)*Math.pow(b,e);
sum=sum+(long)d;
}
//print the result
System.out.println("an-bn= "+sum*c);
}
}

Output:

a= 3
b= 2
n= 4
an-bn= 65

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