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