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 = 1568Input: 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++
// 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 numberslong 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 Programint 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 numbersimport 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 numbersdef 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 Coden = 5;print(evenPowerSum(n));# This is contributed by mits. |
C#
// C# Program to find the sum of fourth powers of// first n even natural numbersusing 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 numbersfunction 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.?> |
Javascript
<script>// JavaScript 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 numbersfunction evenPowerSum( n){ let sum = 0; for (let i = 1; i <= n; i++) { // made even number let j = 2 * i; sum = sum + (j * j * j * j); } return sum;}// Driven Program let n = 5; document.write(evenPowerSum(n)); // This code is contributed by Rajput-Ji </script> |
Output
15664
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++
// 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 numberslong long int evenPowerSum(int n){ return (8 * n * (n + 1) * (2 * n + 1) * (3 * n * n + 3 * n - 1)) / 15;}// Driven Programint 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 numbersimport 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 numbersdef evenPowerSum(n): return (8 * n * (n + 1) * (2 * n + 1) * (3 * n * n + 3 * n - 1)) / 15;# Driver Coden = 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 numbersusing 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 numbersfunction 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.?> |
Javascript
<script>// Javascript 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; } // Driven Program var n = 4; document.write(evenPowerSum(n));// This code is contributed by Rajput-Ji</script> |
Output
5664
Time Complexity: O(1)
Auxiliary Space: O(1)
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