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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