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# Sum of fifth powers of the first n natural numbers

• Difficulty Level : Basic
• Last Updated : 17 Oct, 2022

Write a program to find the sum of Fifth powers of the first n natural numbers 15 + 25+ 35 + 45+ â€¦â€¦.+ n5 till n-th term.
Examples:

Input  : 4
Output : 1300
15 + 25 + 35 + 45 = 1300

Input  : 6
Output : 12201
15 + 25 + 35 + 45 + 55 + 65

Naive Approach :- In this Simple finding the fifth powers of the first n natural numbers is iterate a loop from 1 to n time. like suppose n=5. and store in sum variable.
(1*1*1*1*1)+(2*2*2*2*2)+(3*3*3*3*3)+(4*4*4*4*4) = 1300

## C++

 `// CPP Program to find the sum of fifth powers` `// of first n natural numbers` `#include ` `using` `namespace` `std;`   `// calculate the sum of fifth power of` `// first n natural numbers` `long` `long` `int` `fifthPowerSum(``int` `n)` `{` `    ``long` `long` `int` `sum = 0;` `    ``for` `(``int` `i = 1; i <= n; i++)` `        ``sum = sum + (i * i * i * i * i);` `    ``return` `sum;` `}`   `// Driven Program` `int` `main()` `{` `    ``int` `n = 6;` `    ``cout << fifthPowerSum(n) << endl;` `    ``return` `0;` `}`

## Java

 `// Java Program to find the ` `// sum of fifth  powers of ` `// first n natural numbers` `import` `java.io.*;`   `class` `GFG ` `{` `    ``// calculate the sum of fifth` `    ``// power of first n natural ` `    ``// numbers` `    ``static` `long` `fifthPowerSum(``int` `n)` `    ``{` `        ``long` `sum = ``0``;` `        ``for` `(``int` `i = ``1``; i <= n; i++)` `            ``sum = sum + (i * i * i * i * i);` `        ``return` `sum;` `    ``}` `    `  `    ``// Driven Program` `    ``public` `static` `void` `main(String args[])` `    ``{` `        ``int` `n = ``6``;` `        ``System.out.println(fifthPowerSum(n));` `    ``}` `}`   `// This code is contributed by ` `// Nikita Tiwari.`

## Python3

 `# Python 3 Program to find the` `# sum of fifth powers of first` `# n natural numbers`   `# calculate the sum of fifth ` `# power of first n natural ` `# numbers` `def` `fifthPowerSum(n) :`   `    ``sm ``=` `0` `    `  `    ``for` `i ``in` `range``(``1``, n``+``1``) :` `        ``sm ``=` `sm ``+` `(i ``*` `i ``*` `i ``*` `i ``*` `i)` `    `  `    ``return` `sm`   `# Driven Program` `n ``=` `6` `print``(fifthPowerSum(n))`   `# This code is contributed ` `# by Nikita Tiwari.`

## C#

 `// C# Program to find the ` `// sum of fifth powers of ` `// first n natural numbers` `using` `System;`   `class` `GFG ` `{` `    ``// calculate the sum of fifth` `    ``// power of first n natural ` `    ``// numbers` `    ``static` `long` `fifthPowerSum(``int` `n)` `    ``{` `        ``long` `sum = 0;` `        ``for` `(``int` `i = 1; i <= n; i++)` `            ``sum = sum + (i * i * i * i * i);`   `        ``return` `sum;` `    ``}` `    `  `    ``// Driven Program` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `n = 6;` `        ``Console.Write(fifthPowerSum(n));` `    ``}` `}`   `// This code is contributed by ` `// vt_m.`

## PHP

 ``

## Javascript

 ``

Output

```12201
```

Time complexity: O(N)
Auxiliary Space: O(1)

Efficient Approach :- An efficient solution is to use direct mathematical formula which is :

```(2*n6+6*n5+5*n4 - n2)/12

OR (Can also be written as)

(1/6)n6 + (1/2)n5 + (5/12)n4 â€“ (1/12)n2. ```

## C++

 `// CPP Program to find the sum of fifth power` `// of first n natural numbers` `#include ` `using` `namespace` `std;`   `// calculate the sum of fifth power of first n natural numbers` `long` `long` `int` `fifthPowerSum(``int` `n)` `{` `    ``return` `((2 * n * n * n * n * n * n) +` `           ``(6 * n * n * n * n * n) + ` `           ``(5 * n * n * n * n) -` `           ``(n * n)) / 12;` `}`   `// Driven Program` `int` `main()` `{` `    ``int` `n = 5;` `    ``cout << fifthPowerSum(n) << endl;` `    ``return` `0;` `}`

## Java

 `// Java Program to find the sum of fifth power` `// of first n natural numbers` `import` `java.io.*;`   `class` `GFG {` `    `  `    ``// calculate the sum of fifth power` `    ``//of first n natural numbers` `    ``static` `long` `fifthPowerSum(``int` `n)` `    ``{` `        ``return` `((``2` `* n * n * n * n * n * n) +` `            ``(``6` `* n * n * n * n * n) + ` `            ``(``5` `* n * n * n * n) -` `            ``(n * n)) / ``12``;` `    ``}` `    `  `    ``// Driven Program` `    ``public` `static` `void` `main(String args[])` `    ``{` `        ``int` `n = ``5``;` `        ``System.out.println(fifthPowerSum(n));` `    ``}` `}`   ` ``/*This code is contributed by Nikita Tiwari.*/`

## Python3

 `# Python 3 Program to find the ` `# sum of fifth power of first ` `# n natural numbers`   `# Calculate the sum of fifth ` `# power of first n natural ` `# numbers` `def` `fifthPowerSum(n) :` `    ``return` `((``2` `*` `n ``*` `n ``*` `n ``*` `n ``*` `n ``*` `n) ``+` `            ``(``6` `*` `n ``*` `n ``*` `n ``*` `n ``*` `n) ``+` `            ``(``5` `*` `n ``*` `n ``*` `n ``*` `n) ``-` `            ``(n ``*` `n)) ``/``/` `12`     `# Driven Program` `n ``=` `5` `print``(fifthPowerSum(n))`   `# This code is contributed by Nikita Tiwari.`

## C#

 `// C# Program to find the sum ` `// of fifth power of first n ` `// natural numbers` `using` `System;`   `class` `GFG {` `    `  `    ``// calculate the sum of fifth power` `    ``// of first n natural numbers` `    ``static` `long` `fifthPowerSum(``int` `n)` `    ``{` `        ``return` `((2 * n * n * n * n * n * n) +` `            ``(6 * n * n * n * n * n) + ` `            ``(5 * n * n * n * n) -` `            ``(n * n)) / 12;` `    ``}` `    `  `    ``// Driven Program` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `n = 5;` `        ``Console.Write(fifthPowerSum(n));` `    ``}` `}`   `/*This code is contributed by vt_m.*/`

## PHP

 ``

## Javascript

 ``

Output

```4425
```

Time complexity: O(1)
Auxiliary Space: O(1)

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