Sum of fifth powers of the first n natural numbers

26 Mar, 2021
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
 
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++
Java
Python3
C#
PHP
Javascript
// CPP Program to find the sum of fifth powers// of first n natural numbers#include <bits/stdc++.h>using namespace std; // calculate the sum of fifth power of// first n natural numberslong 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 Programint main(){    int n = 6;    cout << fifthPowerSum(n) << endl;    return 0;}
// Java Program to find the// sum of fifth  powers of// first n natural numbersimport 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.
# 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# numbersdef fifthPowerSum(n) :     sm = 0         for i in range(1, n+1) :        sm = sm + (i * i * i * i * i)         return sm # Driven Programn = 6print(fifthPowerSum(n)) # This code is contributed# by Nikita Tiwari.
// C# Program to find the// sum of fifth powers of// first n natural numbersusing 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// PHP Program to find// the sum of fifth powers// of first n natural numbers // calculate the sum of// fifth power of// first n natural numbersfunction fifthPowerSum($n){    $sum = 0;    for ($i = 1; $i <= $n; $i++)        $sum = $sum + ($i * $i * $i *                             $i * $i);    return $sum;} // Driver Code$n = 6;echo(fifthPowerSum($n)); // This code is contributed by Ajit.?>
<script> // javascript Program to find the sum of fifth powers// of first n natural numbers  // calculate the sum of fifth power of// first n natural numbersfunction fifthPowerSum( n){    let sum = 0;    for (let i = 1; i <= n; i++)        sum = sum + (i * i * i * i * i);    return sum;} // Driven Program     let n = 6;     document.write(fifthPowerSum(n)); // This code contributed by aashish1995 </script>
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++
Java
Python3
C#
PHP
Javascript
// CPP Program to find the sum of fifth power// of first n natural numbers#include <bits/stdc++.h>using namespace std; // calculate the sum of fifth power of first n natural numberslong 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 Programint main(){    int n = 5;    cout << fifthPowerSum(n) << endl;    return 0;}
// Java Program to find the sum of fifth power// of first n natural numbersimport 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.*/
# 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# numbersdef 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 Programn = 5print(fifthPowerSum(n)) # This code is contributed by Nikita Tiwari.
// C# Program to find the sum// of fifth power of first n// natural numbersusing 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// PHP Program to find// the sum of fifth power// of first n natural numbers // calculate the sum of// fifth power of first// n natural numbersfunction fifthPowerSum($n){    return ((2 * $n * $n * $n * $n * $n * $n) +            (6 * $n * $n * $n * $n * $n) +            (5 * $n * $n * $n * $n) -            ($n * $n)) / 12;} // Driver Code$n = 5;echo(fifthPowerSum($n)); // This code is contributed by Ajit.?>
<script>// JavaScript Program to find the sum of fifth power// of first n natural numbers // calculate the sum of fifth power of first n natural numbersfunction 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     let n = 5;    document.write(fifthPowerSum(n) + "<br>");     // This code is contributed by Mayank Tyagi </script>
Output: 
 4425
Time complexity : O(1) 
jit_t
aashish1995
mayanktyagi1709
number-theory
series
series-sum
Mathematical
number-theory
Mathematical
series
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