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# Sum of fifth powers of the first n natural numbers

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 : 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 – (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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