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 : 
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++

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// 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 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;
}

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Java

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// 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.

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Python3

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# 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.

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C#

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// 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.

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PHP

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<?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 numbers
function 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.
?>

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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++

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// 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 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;
}

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Java

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// 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.*/

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Python3

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# 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.

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C#

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// 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.*/

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PHP

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<?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 numbers
function 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.
?>

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Output:

 4425

Time complexity : O(1)



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Improved By : jit_t