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Sum of Series (n^2-1^2) + 2(n^2-2^2) +....n(n^2-n^2)

Last Updated : 23 Nov, 2022
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Program for finding the sum of the nth term of the series (n^2-1^2) + 2(n^2-2^2) + 3(n^2-3^2) + ....n(n^2-n^2) 

Examples: 

Input : 2
Output :3

Input :5
Output :150

To solve this problem we have the formula ((1/4)*n2*(n2-1)). We can prove the formula using mathematical induction. 

Example n = 2
result = ((1/4)*2^2*(2^2-1))
       = ((0.25)*4*(4-1))
       = ((0.25)*4*3
       = 3 ans.


 Below is the implementation:

C++ 
// CPP Program to finding the
// sum of the nth series
#include <bits/stdc++.h>
using namespace std;

// function that calculate
// the sum of the nth series
int sum_series(int n)
{
    int nSquare = n * n;

    // using formula of the nth term
    return nSquare * (nSquare - 1) / 4;
}

// driver function
int main()
{
    int n = 2;
    cout << sum_series(n) << endl;
    return 0;
}
Java 
// javaProgram to finding the
// sum of the nth series
import java.io.*;

class GFG {
    
    // function that calculate
    // the sum of the nth series
    static int sum_series(int n)
    {
        int nSquare = n * n;
    
        // using formula of the nth term
        return nSquare * (nSquare - 1) / 4;
    }

    // Driver function
    public static void main (String[] args) 
    {
        int n = 2;
        System.out.println( sum_series(n)) ;
    
    }
    
}
// This article is contributed by vt_m
Python3 
# Python 3 Program to finding
# the sum of the nth series

# function that calculate
# the sum of the nth series
def sum_series(n):

    nSquare = n * n 

    # Using formula of the
    # nth term
    return int(nSquare * (nSquare - 1) / 4) 

# Driver function
n = 2
print(sum_series(n))

# This code is contributed by Smitha Dinesh Semwal
C# 
// C# program to finding the
// sum of the nth series
using System;

class GFG {
    
    // Function that calculate
    // the sum of the nth series
    static int sum_series(int n)
    {
        int nSquare = n * n;
    
        // Using formula of the nth term
        return nSquare * (nSquare - 1) / 4;
    }

    // Driver Code
    public static void Main () 
    {
        int n = 2;
        Console.Write( sum_series(n)) ;
    
    }
}

// This code is contributed by vt_m
PHP 
<?php
// PHP Program to finding the
// sum of the nth series

// function that calculate
// the sum of the nth series
function sum_series($n)
{
    $nSquare = $n * $n;

    // using formula of the nth term
    return $nSquare * ($nSquare - 1) / 4;
}

// Driver Code
$n = 2;
echo(sum_series($n));

// This code is contributed by Ajit.
?>
JavaScript 
<script>

// JavaScript Program to finding the
// sum of the nth series

    // function that calculate
    // the sum of the nth series
    function sum_series(n)
    {
        let nSquare = n * n;
      
        // using formula of the nth term
        return nSquare * (nSquare - 1) / 4;
    }
  
 
// Driver code

        let n = 2;
        document.write( sum_series(n)) ;

</script>

Output
3

Time complexity: O(1)
Auxiliary space: O(1)


A

Ajay Puri
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