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Sum of fourth power of first n even natural numbers
  • Last Updated : 06 Aug, 2018

Write a program to find the sum of fourth power of first n even natural numbers.
24 + 44 + 64 + 84 + 104 +………+2n4
Examples:

Input  :   3
Output :  1568
24 +44 +64 = 1568
Input  :   6
Output :  36400
24 + 44 + 64 + 84 + 104 + 124 

Naive Approach :- In this Simple finding the fourth powers of the first n even natural numbers is iterate a loop from 1 to n time. Every i’th iteration store in variable and continue till (i!=n). This is take a O(N) Time Complexity.

C++




// CPP Program to find the sum of fourth powers of
// first n even natural numbers
#include <bits/stdc++.h>
using namespace std;
  
// calculate the sum of fourth power of first n even
// natural numbers
long long int evenPowerSum(int n)
{
    long long int sum = 0;
    for (int i = 1; i <= n; i++) {
  
        // made even number
        int j = 2 * i;
        sum = sum + (j * j * j * j);
    }
    return sum;
}
  
// Driven Program
int main()
{
    int n = 5;
    cout << evenPowerSum(n) << endl;
    return 0;
}


Java




// Java Program to find the sum of fourth powers of
// first n even natural numbers
  
import java.io.*;
  
class GFG {
      
    // calculate the sum of fourth power of first 
    // n even natural numbers
    static long evenPowerSum(int n)
    {
        long sum = 0;
        for (int i = 1; i <= n; i++)
        {
      
            // made even number
            int j = 2 * i;
            sum = sum + (j * j * j * j);
        }
          
        return sum;
    }
  
    // Driven Program
    public static void main (String[] args) {
          
        int n = 5;
        System.out.println(evenPowerSum(n));
    }
}
  
/*This code is contributed by vt_m.*/


Python3




# Python3 Program to find 
# the sum of fourth powers of
# first n even natural numbers
  
# calculate the sum of fourth 
# power of first n even
# natural numbers
def evenPowerSum(n):
    sum = 0;
    for i in range(1, n + 1):
          
        # made even number
        j = 2 * i;
        sum = sum + (j * j * j * j);
    return sum;
  
# Driver Code
n = 5;
print(evenPowerSum(n));
  
# This is contributed by mits.


C#




// C# Program to find the sum of fourth powers of
// first n even natural numbers
using System;
  
class GFG {
  
    // calculate the sum of fourth power of 
    // first n even natural numbers
    static long evenPowerSum(int n)
    {
          
        long sum = 0;
        for (int i = 1; i <= n; i++) {
  
            // made even number
            int j = 2 * i;
            sum = sum + (j * j * j * j);
        }
          
        return sum;
    }
  
    // Driven Program
    public static void Main()
    {
        int n = 5;
          
        Console.Write(evenPowerSum(n));
    }
}
  
// This code is contributed by vt_m.


PHP




<?php
// PHP Program to find the 
// sum of fourth powers of
// first n even natural numbers
  
// calculate the sum of 
// fourth power of first 
// n even natural numbers
function evenPowerSum($n)
{
    $sum = 0;
    for ($i = 1; $i <= $n; $i++)
    {
  
        // made even number
        $j = 2 * $i;
        $sum = $sum + ($j * $j * $j * $j);
    }
    return $sum;
}
  
// Driver Code
$n = 5;
echo(evenPowerSum($n));
  
// This code is contributed by Ajit.
?>



Output:

 15664

Time Complexity : O(n)



Efficient Approach :- An efficient solution is to use direct mathematical formula which is derived below, This is take only O(1) Time Complexity.

Sum of fourth power of first n even natural number = 8*(n*(n+1)*(2*n+1)(3*n2+3*n -1))/15

How does this formula work?
Sum of fourth power of natural numbers is = (n(n+1)(2n+1)(3n2+3n-1))/30
we need even natural number so we multiply each term 24
= 24(14 + 24 + 34 + ………… +n4)
= (24 + 44 + 64 + ………… +2n4)
= 24*(sum of fourth power natural number)
= 16*(n*(n+1)*(2*n+1)(3*n2+3*n -1))/30
= 8*(n*(n+1)*(2*n+1)(3*n2+3*n -1))/15

C++




// CPP Program to find the sum of fourth powers of
// first n even natural numbers
#include <bits/stdc++.h>
using namespace std;
  
// calculate the sum of fourth power of first n 
// even natural numbers
long long int evenPowerSum(int n)
{
    return (8 * n * (n + 1) * (2 * n + 1) * 
          (3 * n * n + 3 * n - 1)) / 15;
}
  
// Driven Program
int main()
{
    int n = 4;
    cout << evenPowerSum(n) << endl;
    return 0;
}


Java




// JAVA Program to find the sum of fourth powers of
// first n even natural numbers
  
import java.io.*;
  
class GFG {
          
    // calculate the sum of fourth power of first n 
    // even natural numbers
    static long evenPowerSum(int n)
    {
        return (8 * n * (n + 1) * (2 * n + 1) * 
                   (3 * n * n + 3 * n - 1)) / 15;
    }
      
    // Driven Program
    public static void main (String[] args) {
          
        int n = 4;
        System.out.println(evenPowerSum(n));
    }
}
  
/* This code is contributed by vt_m. */


Python3




# Python3 Program to find 
# the sum of fourth powers 
# of first n even natural 
# numbers
  
# calculate the sum of 
# fourth power of first n 
# even natural numbers
def evenPowerSum(n):
    return (8 * n * (n + 1) * 
           (2 * n + 1) * (3 *
            n * n + 3 * n - 1)) / 15;
  
# Driver Code
n = 4;
print (int(evenPowerSum(n)));
  
# This code is contributed by mits


C#




// C# Program to find the sum of fourth powers of
// first n even natural numbers
  
using System;
  
class GFG {
  
    // calculate the sum of fourth power of first n
    // even natural numbers
    static long evenPowerSum(int n)
    {
        return (8 * n * (n + 1) * (2 * n + 1) *
                     (3 * n * n + 3 * n - 1)) / 15;
    }
  
    // Driven Program
    public static void Main()
    {
        int n = 4;
          
        Console.Write(evenPowerSum(n));
    }
}
  
/* This code is contributed by vt_m.*/


PHP




<?php
// PHP Program to find the
// sum of fourth powers of
// first n even natural numbers
  
// calculate the sum of 
// fourth power of first n 
// even natural numbers
function evenPowerSum($n)
{
    return (8 * $n * ($n + 1) * 
           (2 * $n + 1) * 
           (3 * $n * $n + 3 * 
            $n - 1)) / 15;
}
  
// Driver Code
$n = 4;
echo(evenPowerSum($n));
  
// This code is contributed by Ajit.
?>



Output:

5664

Time Complexity : O(1)

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