# Java Program to Find the Sum of Series (1*2) + (2*3) + (3*4) + …… + N

In the previous article, we have discussed about Java Program to Print Series 9 18 27 36 45 54 …N

In this article we are going to see how to find the sum of the series (1*2) + (2*3) + (3*4) + …… + N by using java programming language.

## Java Program to Find the Sum of Series (1*2) + (2*3) + (3*4) + …… + N

On observing the pattern carefully, we can see each term is like (a*b) format. Value of ‘a‘ starts from 1 and ‘b‘ value is like ‘a+1‘ and in next term of series previous ‘b‘ value is the value of ‘a

Example:

N = 5

1*2 + 2*3 + 3*4 + 4*5 + 5*6 = 2+6+12+20+30 = 70

Let’s see different ways to find the sum of the series (1*2) + (2*3) + (3*4) + …… + N

### Method-1: Java Program to Find the Sum of Series (1*2) + (2*3) + (3*4) + …… + N By Using For Loop

Approach:

• Create Scanner class object.
• Declare an integer variable say ‘n’ which holds the value of number of terms in series.
• Declare an integer variable say ‘sum‘ and initialize it to 0.
• Prompt the user to enter a number as value of n.
• Use a for loop from i=1 to i<=n
• Inside for loop we will multiply i*(i+1) and add with sum.
• Print the result.

Program:

import java.util.*;
public class Main
{
public static void main(String args[])
{
//creating object of Scanner class
Scanner s = new Scanner(System.in);
//Taking input of number of elements in the series
System.out.println("Enter the value of last number 'n' ");
int n = s.nextInt();
//for loop to print the series
int sum = 0;
for (int i = 1; i <= n; i++)
sum += i * (i + 1);
System.out.println("Sum of the series is " + sum);
}
}

Output:

Enter the value of last number 'n'
5
Sum of the series is 70

### Method-2: Java Program to Find the Sum of Series (1*2) + (2*3) + (3*4) + …… + N By Using While Loop

Approach:

• Create Scanner class object.
• Declare an integer variable say ‘n’ which holds the value of number of terms in series.
• Declare an integer variable say ‘sum‘ and initialize it to 0.
• Prompt the user to enter a number as value of n.
• Use a while loop from i=1 till i<=n
• Inside while loop we will multiply i*(i+1) and add with sum.
• Print the result.

Program:

import java.util.*;
public class Main
{
public static void main(String args[])
{
//creating object of Scanner class
Scanner s = new Scanner(System.in);
//Taking input of number of elements in the series
System.out.println("Enter the value of last number 'n' ");
int n = s.nextInt();
// while loop to print the series
int sum = 0;
int i = 1;
while(i <= n)
{
sum += i * (i + 1);
i++;
}
System.out.println("Sum of the series is " + sum);
}
}

Output:

Enter the value of last number 'n'
9
Sum of the series is 330

### Method-3: Java Program to Find the Sum of Series (1*2) + (2*3) + (3*4) + …… + N By Using User Defined Method

Approach:

• Create Scanner class object.
• Declare an integer variable say ‘n’ which holds the value of number of terms in series.
• Prompt the user to enter a number as value of n.
• Call a user defined method m1() and pass ‘n‘ as parameter.
• Inside method declare an integer variable say ‘sum‘ and initialize it to 0.
• Use a for loop from i=1 to i<=n
• Inside for loop we will multiply i*(i+1) and add with sum.
• Print the result.

Program:

import java.util.*;
public class Main
{
public static void main(String[] args)
{
// creating object of scanner class
Scanner s = new Scanner(System.in);
//Taking input of number of elements in the series
System.out.println("Enter the value of last exponent 'n' ");
int n = s.nextInt();
// calling m1 method to print the series
m1(n);
}
public static void m1(int n)
{
//for loop to print the series
int sum = 0;
for (int i = 1; i <= n; i++)
sum += i * (i + 1);
System.out.println("Sum of the series is  " + sum);
}
}

Output:

Enter the value of last exponent 'n'
10
Sum of the series is 440

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