Prerequisite: Recursion in Java

In the previous article, we have discussed about Java Program to Find Digital Roots of a Number by Using Recursion

In this program we are going to see how to find sum of the series by using Recursion by Java programming language.

## Java Program to Find Sum of Series 1^2+2^2+3^2+…+n^2 by using Recursion

Let’s understand it with an example.

Lets assume the nth term of the series n = 4 Sum of the series = 1^2+2^2+3^2+4^2 = 1+4+9+16 = 30

Now let’s see different ways to find sum of the series by using Recursion.

### Method-1: Java Program to Find Sum of Series 1^2+2^2+3^2+…+n^2 By Using Static Input and Recursion

**Approach:**

- Declare and initialize an integer variable say ‘
`n`

’ - Call a user defined method
`sumSeries()`

method and pass ‘`n`

’ as parameter to find sum of the series . - Inside the user defined method we will check if the nth term is 0 or not. If the nth term is 0 then the sum of the series is 0 else find the sum of the series by calling
`sumSeries()`

method recursively. - Now the value of the user defined method
`sumSeries()`

is stored in an integer variable say ‘`sum`

’. - Print the value of the sum of the series.

**Program:**

import java.util.*; import java.io.*; public class Main { public static void main(String[] args) { // declare and initialize an integer variable ‘n’ = 4 int n = 4; //call sumSeries() method to find the sum of the series int sum = sumSeries(n); // print the result System.out.println("The sum of the series is: "+sum); } //sumSeries() method static int sumSeries(int n) { // if the nth term is 0 then the sum of the series is 0 if(n == 0) return 0; // else find the sum of the series by calling sumSeries() method recursively else return (n*n) + sumSeries(n-1); } }

Output: The sum of the series is: 30

### Method-2: Java Program to Find Sum of Series 1^2+2^2+3^2+…+n^2 By Using User Input and Recursion

**Approach:**

- Declare an integer variable say ‘
`n`

’ - Prompt the user to enter a number.
- Call a user defined method
`sumSeries()`

method and pass ‘`n`

’ as parameter to find sum of the series . - Inside the user defined method we will check if the nth term is 0 or not. If the nth term is 0 then the sum of the series is 0 else find the sum of the series by calling
`sumSeries()`

method recursively. - Now the value of the user defined method
`sumSeries()`

is stored in an integer variable say ‘`sum`

’. - Print the value of the sum of the series.

**Program:**

import java.util.*; import java.io.*; public class Main { public static void main(String[] args) { // create a scanner class Scanner s = new Scanner(System.in); System.out.println("Enter the nth term of the series:"); int n = s.nextInt(); //defined sumSeries() method to find the sum of the series int sum = sumSeries(n); // print the result System.out.println("The sum of the series is: "+sum); } //sumSeries() method static int sumSeries(int n) { // if the nth term is 0 then the sum of the series is 0 if(n == 0) return 0; // else find the sum of the series by calling sumSeries() method recursively else return (n*n) + sumSeries(n-1); } }

Output: Enter the nth term of the series: 9 The sum of the series is: 285

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