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

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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)



Last Updated : 23 Nov, 2022
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