Write a program to find the sum of fourth powers of the first n natural numbers 14 + 24 + 34 + 44 + …….+ n4 till n-th term.
Examples :
Input : 4 Output : 354 14 + 24 + 34 + 44 = 354 Input : 6 Output : 2275 14 + 24 + 34 + 44+ 54+ 64 = 2275
Naive Approach :- Simple finding the fourth powers of the first n natural numbers is iterate a loop from 1 to n time. like suppose n=4.
(1*1*1*1)+(2*2*2*2)+(3*3*3*3)+(4*4*4*4) = 354
C++
// CPP Program to find the sum of fourth powers// of first n natural numbers#include <bits/stdc++.h>using namespace std;// Return the sum of fourth power of first n// natural numberslong long int fourthPowerSum(int n){ long long int sum = 0; for (int i = 1; i <= n; i++) sum = sum + (i * i * i * i); return sum;}// Driven Programint main(){ int n = 6; cout << fourthPowerSum(n) << endl; return 0;} |
Java
// Java Program to find the// sum of fourth powers of // first n natural numbersimport java.io.*;import java.util.*;class GFG { // Return the sum of fourth // power of first n natural // numbers static long fourthPowerSum(int n) { long sum = 0; for (int i = 1; i <= n; i++) sum = sum + (i * i * i * i); return sum; } public static void main (String[] args) { int n = 6; System.out.println(fourthPowerSum(n)); }}// This code is contributed by Gitanjali. |
Python3
# Python3 Program to find the# sum of fourth powers of first# n natural numbersimport math # Return the sum of fourth power of # first n natural numbersdef fourthPowerSum( n): sum = 0 for i in range(1, n+1) : sum = sum + (i * i * i * i) return sum# Driver methodn=6print (fourthPowerSum(n))# This code is contributed by Gitanjali. |
C#
// C# program to find the// sum of fourth powers of // first n natural numbersusing System;class GFG { // Return the sum of fourth power // of first n natural numbers static long fourthPowerSum(int n) { long sum = 0; for (int i = 1; i <= n; i++) sum = sum + (i * i * i * i); return sum; } public static void Main () { int n = 6; Console.WriteLine(fourthPowerSum(n)); }}// This code is contributed by vt_m. |
PHP
<?php// PHP Program to find th// sum of fourth powers// of first n natural numbers// Return the sum of fourth// power of first n// natural numbersfunction fourthPowerSum($n){ $sum = 0; for ($i = 1; $i <= $n; $i++) $sum = $sum + ($i * $i * $i * $i); return $sum;}// Driver Code$n = 6;echo(fourthPowerSum($n));// This code is contributed by Ajit.?> |
Javascript
<script>// javascript Program to find the sum of fourth powers// of first n natural numbers// Return the sum of fourth power of first n// natural numbersfunction fourthPowerSum( n){ let sum = 0; for (let i = 1; i <= n; i++) sum = sum + (i * i * i * i); return sum;}// Driven Program let n = 6; document.write(fourthPowerSum(n));// This code contributed by aashish1995 </script> |
Output:
2275
Complexity Analysis:
Time Complexity : O(n) ,as there is single loop used inside fourthpowersum() function.
Space Complexity: O(1) , as there is no extra space used.
Efficient Approach :- An efficient solution is to use direct mathematical formula which is 1/30n(n+1)(2n+1)(3n2+3n+1) or it is also write (1/5)n5 + (1/2)n4 + (1/3)n3 – (1/30)n. This solution take O(1) time.
C++
// CPP Program to find the sum of fourth power of first// n natural numbers#include <bits/stdc++.h>using namespace std;// Return the sum of fourth power of first n natural// numberslong long int fourthPowerSum(int n){ return ((6 * n * n * n * n * n) + (15 * n * n * n * n) + (10 * n * n * n) - n) / 30;}// Driven Programint main(){ int n = 6; cout << fourthPowerSum(n) << endl; return 0;} |
Java
// Java Program to find the// sum of fourth powers of// first n natural numbersimport java.io.*;import java.util.*;class GFG { // Return the sum of // fourth power of first // n natural numbers static long fourthPowerSum(int n) { return ((6 * n * n * n * n * n) + (15 * n * n * n * n) + (10 * n * n * n) - n) / 30; } public static void main (String[] args) { int n = 6; System.out.println(fourthPowerSum(n)); }}// This code is contributed by Gitanjali. |
Python3
# Python3 Program to # find the sum of # fourth powers of # first n natural numbersimport math # Return the sum of # fourth power of # first n natural # numbersdef fourthPowerSum(n): return ((6 * n * n * n * n * n) + (15 * n * n * n * n) + (10 * n * n * n) - n) / 30 # Driver methodn=6print (fourthPowerSum(n))# This code is contributed by Gitanjali. |
C#
// C# Program to find the// sum of fourth powers of// first n natural numbersusing System;class GFG { // Return the sum of // fourth power of first // n natural numbers static long fourthPowerSum(int n) { return ((6 * n * n * n * n * n) + (15 * n * n * n * n) + (10 * n * n * n) - n) / 30; } public static void Main () { int n = 6; Console.Write(fourthPowerSum(n)); }}// This code is contributed by vt_m. |
PHP
<?php// PHP Program to find the sum // of fourth power of first// n natural numbers// Return the sum of fourth// power of first n natural// numbersfunction fourthPowerSum($n){ return ((6 * $n * $n * $n * $n * $n) + (15 * $n * $n * $n * $n) + (10 * $n * $n * $n) - $n) / 30;}// Driver Code$n = 6;echo(fourthPowerSum($n));// This code is contributed by Ajit.?> |
Javascript
<script>// javascript Program to find the// sum of fourth powers of// first n natural numbers // Return the sum of // fourth power of first// n natural numbersfunction fourthPowerSum(n){ return ((6 * n * n * n * n * n) + (15 * n * n * n * n) + (10 * n * n * n) - n) / 30;}var n = 6;document.write(fourthPowerSum(n)); // This code is contributed by 29AjayKumar </script> |
Output:
2275
Complexity Analysis:
Time Complexity : O(1)
Space Complexity: O(1)
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