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# Sum of fourth powers of the first n natural numbers

• Last Updated : 31 Mar, 2021

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 forth powers``// of first n natural numbers``#include ``using` `namespace` `std;` `// Return the sum of forth power of first n``// natural numbers``long` `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 Program``int` `main()``{``    ``int` `n = 6;``    ``cout << fourthPowerSum(n) << endl;``    ``return` `0;``}`

## Java

 `// Java Program to find the``// sum of forth powers of``// first n natural numbers``import` `java.io.*;``import` `java.util.*;` `class` `GFG {``    ` `    ``// Return the sum of forth``    ``// 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 forth powers of first``# n natural numbers``import` `math` `# Return the sum of forth power of``# first n natural numbers``def` `fourthPowerSum( n):` `    ``sum` `=` `0``    ``for` `i ``in` `range``(``1``, n``+``1``) :``        ``sum` `=` `sum` `+` `(i ``*` `i ``*` `i ``*` `i)``    ``return` `sum``# Driver method``n``=``6``print` `(fourthPowerSum(n))` `# This code is contributed by Gitanjali.`

## C#

 `// C# program to find the``// sum of forth powers of``// first n natural numbers``using` `System;` `class` `GFG {``    ` `    ``// Return the sum of forth 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

 ``

## Javascript

 ``

Output:

`2275`

Time Complexity : O(n)
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 forth power of first``// n natural numbers``#include ``using` `namespace` `std;` `// Return the sum of forth power of first n natural``// numbers``long` `long` `int` `fourthPowerSum(``int` `n)``{``    ``return` `((6 * n * n * n * n * n) +``            ``(15 * n * n * n * n) +``            ``(10 * n * n * n) - n) / 30;``}` `// Driven Program``int` `main()``{``    ``int` `n = 6;``    ``cout << fourthPowerSum(n) << endl;``    ``return` `0;``}`

## Java

 `// Java Program to find the``// sum of forth powers of``// first n natural numbers``import` `java.io.*;``import` `java.util.*;` `class` `GFG {``    ` `    ``// Return the sum of``    ``// forth 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``# forth powers of``# first n natural numbers``import` `math` `# Return the sum of``# forth power of``# first n natural``# numbers``def` `fourthPowerSum(n):` `    ``return` `((``6` `*` `n ``*` `n ``*` `n ``*` `n ``*` `n) ``+``            ``(``15` `*` `n ``*` `n ``*` `n ``*` `n) ``+``            ``(``10` `*` `n ``*` `n ``*` `n) ``-` `n) ``/` `30``    ` `# Driver method``n``=``6``print` `(fourthPowerSum(n))` `# This code is contributed by Gitanjali.`

## C#

 `// C# Program to find the``// sum of forth powers of``// first n natural numbers``using` `System;` `class` `GFG {``    ` `    ``// Return the sum of``    ``// forth 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

 ``

## Javascript

 ``

Output:

`2275`

Time Complexity : O(1)

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