# Java Program - Calculate sum of Squares of Natural numbers

In Mathematics, the natural numbers are all positive numbers which is used for counting like 1, 2, 3, 4, and so on. The smallest natural number is 1.

Objective: Write a Java program which returns sum of squares of natural numbers starting from 1 to given natural number n, (12 + 22 + 32 + ... + n2).

### Method 1: Using while loop

The example below shows how to use while loop to calculate sum of squares of first n natural numbers.

```public class MyClass {
public static void main(String[] args) {
int n = 10;
int i = 1;
int sum = 0;

//calculating sum of squares from 1 to n
while(i <= n) {
sum += i*i;
i++;
}

System.out.println("Sum is: " + sum);
}
}
```

The above code will give the following output:

```Sum is: 385
```

### Method 2: Using for loop

The same can be achieved using for loop. Consider the example below:

```public class MyClass {
public static void main(String[] args) {
int n = 10;
int sum = 0;

//calculating sum of squares from 1 to n
for(int i = 1; i <= n; i++)
sum += i*i;

System.out.println("Sum is: " + sum);
}
}
```

The above code will give the following output:

```Sum is: 385
```

### Method 3: Using Recursion

Similarly, recursion can be used to calculate the sum.

```public class MyClass {
//recursive method
static int Sum(int n) {
if(n == 1)
return 1;
else
return (n*n + Sum(n-1));
}

public static void main(String[] args) {
System.out.println("Sum of Squares of first 10 natural numbers: " + Sum(10));
System.out.println("Sum of Squares of first 20 natural numbers: " + Sum(20));
}
}
```

The above code will give the following output:

```Sum of Squares of first 10 natural numbers: 385
Sum of Squares of first 20 natural numbers: 2870
```

### Method 4: Using Mathematical Formula

The sum of squares of first n natural numbers can be mathematically expressed as:

```public class MyClass {
public static void main(String[] args) {
int n = 10;

//calculating sum of squares from 1 to n
int sum = n*(n+1)*(2*n+1)/6;

System.out.println("Sum is: " + sum);
}
}
```

The above code will give the following output:

```Sum is: 385
```

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