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

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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