Sum of fourth power of first n even natural numbers
Last Updated :
25 Oct, 2022
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 takes a O(N) Time Complexity.
C++
#include <bits/stdc++.h>
using namespace std;
long long int evenPowerSum( int n)
{
long long int sum = 0;
for ( int i = 1; i <= n; i++) {
int j = 2 * i;
sum = sum + (j * j * j * j);
}
return sum;
}
int main()
{
int n = 5;
cout << evenPowerSum(n) << endl;
return 0;
}
|
Java
import java.io.*;
class GFG {
static long evenPowerSum( int n)
{
long sum = 0 ;
for ( int i = 1 ; i <= n; i++)
{
int j = 2 * i;
sum = sum + (j * j * j * j);
}
return sum;
}
public static void main (String[] args) {
int n = 5 ;
System.out.println(evenPowerSum(n));
}
}
|
Python3
def evenPowerSum(n):
sum = 0 ;
for i in range ( 1 , n + 1 ):
j = 2 * i;
sum = sum + (j * j * j * j);
return sum ;
n = 5 ;
print (evenPowerSum(n));
|
C#
using System;
class GFG {
static long evenPowerSum( int n)
{
long sum = 0;
for ( int i = 1; i <= n; i++) {
int j = 2 * i;
sum = sum + (j * j * j * j);
}
return sum;
}
public static void Main()
{
int n = 5;
Console.Write(evenPowerSum(n));
}
}
|
PHP
<?php
function evenPowerSum( $n )
{
$sum = 0;
for ( $i = 1; $i <= $n ; $i ++)
{
$j = 2 * $i ;
$sum = $sum + ( $j * $j * $j * $j );
}
return $sum ;
}
$n = 5;
echo (evenPowerSum( $n ));
?>
|
Javascript
<script>
function evenPowerSum( n)
{
let sum = 0;
for (let i = 1; i <= n; i++)
{
let j = 2 * i;
sum = sum + (j * j * j * j);
}
return sum;
}
let n = 5;
document.write(evenPowerSum(n));
</script>
|
Time Complexity: O(n)
Auxiliary Space: O(1)
Efficient Approach :- An efficient solution is to use direct mathematical formula which is derived below, This takes 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++
#include <bits/stdc++.h>
using namespace std;
long long int evenPowerSum( int n)
{
return (8 * n * (n + 1) * (2 * n + 1) *
(3 * n * n + 3 * n - 1)) / 15;
}
int main()
{
int n = 4;
cout << evenPowerSum(n) << endl;
return 0;
}
|
Java
import java.io.*;
class GFG {
static long evenPowerSum( int n)
{
return ( 8 * n * (n + 1 ) * ( 2 * n + 1 ) *
( 3 * n * n + 3 * n - 1 )) / 15 ;
}
public static void main (String[] args) {
int n = 4 ;
System.out.println(evenPowerSum(n));
}
}
|
Python3
def evenPowerSum(n):
return ( 8 * n * (n + 1 ) *
( 2 * n + 1 ) * ( 3 *
n * n + 3 * n - 1 )) / 15 ;
n = 4 ;
print ( int (evenPowerSum(n)));
|
C#
using System;
class GFG {
static long evenPowerSum( int n)
{
return (8 * n * (n + 1) * (2 * n + 1) *
(3 * n * n + 3 * n - 1)) / 15;
}
public static void Main()
{
int n = 4;
Console.Write(evenPowerSum(n));
}
}
|
PHP
<?php
function evenPowerSum( $n )
{
return (8 * $n * ( $n + 1) *
(2 * $n + 1) *
(3 * $n * $n + 3 *
$n - 1)) / 15;
}
$n = 4;
echo (evenPowerSum( $n ));
?>
|
Javascript
<script>
function evenPowerSum(n)
{
return (8 * n * (n + 1) * (2 * n + 1)
* (3 * n * n + 3 * n - 1)) / 15;
}
var n = 4;
document.write(evenPowerSum(n));
</script>
|
Time Complexity: O(1)
Auxiliary Space: O(1)
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