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Sum of fifth powers of the first n natural numbers
• Difficulty Level : Basic
• Last Updated : 25 Apr, 2018

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

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

Input  : 6
Output :
15 + 25 + 35 + 45 + 52 + 65
```

## Recommended: Please solve it on PRACTICE first, before moving on to the solution.

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

 ` `

Output:

``` 12201
```

Time complexity : O(N)
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 – (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

 ` `

Output:

``` 4425
```

Time complexity : O(1)

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