Java Program to Add the nth Square Series

The series to work on is as follows:

Illustration

Input : N = 4
Output: 30
Explanation: 12 + 22 + 32 + 42
           = 1 + 4 + 9 + 16
           = 30

Input: N = 5
Output: 55
Explanation: 12 + 22 + 32 + 42 + 52
           = 1 + 4 + 9 + 16 + 25
           = 55

Approaches: Here will be provided with the value up to which sum is computed for the series. in order to do so standard approaches are as follows:

• Naive Approach: Using for loop to compute the value
• Optimize Method: Using the formula to find the sum of the series.

Approach 1: Using loops a maintaining a count in a variable imposing condition inside the loop.

Example: Sum of the series by using for loop and calculate the square at each instance. This is the most naive approach.

Java

// Java Program to Add the nth Square Series

// Importing java input output libraries
import java.io.*;

class GFG {

    // Main driven Program
    public static void main(String args[])
        throws IOException
    {
        // Declaring and initializing holding current sum
        int sum = 0;

        // Declaring VARIABLE holding term
        // Initializing to random value
        // to show output
        int n = 4;

        System.out.println("Enter number of terms:" + n);

        // For-loop for Iterating from 1 and Nth term
        for (int i = 1; i <= n; i++) {

            // finding square of current term and updating
            // current sum
            sum += (i * i);
        }

        // Printing final sum i.e
        // last updated current sum
        System.out.println("Sum for entered N terms:"
                           + sum);
    }
}

Output:

30

Time Complexity: O(N)

Approach 2: In this approach, we will find the sum of the series by using the formula mentioned below. This formula can be used to find the sum of the n^th Square Series and its correctness can be proved through mathematical induction. It is much more optimized the above illustrated. 

1² + 2² + 3² + … + n² = n * (n + 1) * (2 * (n + 1))/6

Example:

Java

// Java Program to Add the nth Square Series

// Importing java input output libraries
import java.io.*;

class GFG {

    // Main driven Program
    public static void main(String args[]) throws IOException {

           // Declaring VARIABLE holding term
           // Initializing to random value
           // to show output
           int n = 4;

         // Finding sum using formula
        int sum = (n * (n + 1) * (2 * n + 1)) / 6;

        // Displaying result
        System.out.println("Sum upto entered N series :"+sum);
    }
}

Output:

30

Time Complexity: O(1)

Auxiliary space: O(1) as it is using constant variables