# Sum of fourth powers of the first n natural numbers

Write a program to find the sum of fourth powers of the first n natural numbers 14 + 24 + 34 + 44 + â€¦â€¦.+ 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 ` `using` `namespace` `std;`   `// Return the sum of fourth 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 fourth powers of ` `// first n natural numbers` `import` `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 numbers` `import` `math `   `# Return the sum of fourth 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 fourth powers of ` `// first n natural numbers` `using` `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

 ``

## Javascript

 ``

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 ` `using` `namespace` `std;`   `// Return the sum of fourth 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 fourth powers of` `// first n natural numbers` `import` `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 numbers` `import` `math `   `# Return the sum of ` `# fourth 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 fourth powers of` `// first n natural numbers` `using` `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

 ``

## Javascript

 ``

Output:

`2275`

Complexity Analysis:
Time Complexity : O(1)

Space Complexity: O(1)

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