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

• Difficulty Level : Easy
• Last Updated : 07 Apr, 2021

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.```

## C++

 `// CPP Program to finding the``// sum of the nth series``#include ``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

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## Javascript

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Output:

`3`

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