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)