# Mean of fourth powers of first N natural numbers

• Last Updated : 06 Oct, 2021

Given a positive integer N, the task is to find the average of the fourth powers of the first N natural numbers.

Examples:

Input: N = 3
Output: 32.6667
Explanation:
The sum of the fourth powers of the first N natural numbers = 14 + 24 + 34 = 1 + 16 + 81 = 98.
Therefore, the average = 98 / 3 = 32.6667.

Input: N = 5
Output: 12

Naive Approach: The simplest approach to solve the given problem is to find the sum of the fourth powers of first N natural numbers and print its value when divided by N.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach   #include  using namespace std;   // Function to find the average of the // fourth power of first N natural numbers double findAverage(int N) {     // Stores the sum of the fourth     // powers of first N natural numbers     double S = 0;       // Calculate the sum of fourth power     for (int i = 1; i <= N; i++) {         S += i * i * i * i;     }       // Return the average     return S / N; }   // Driver Code int main() {     int N = 3;     cout << findAverage(N);       return 0; }

## Java

 // Java program for the above approach class GFG{   // Function to find the average of the // fourth power of first N natural numbers static double findAverage(int N) {           // Stores the sum of the fourth     // powers of first N natural numbers     double S = 0;       // Calculate the sum of fourth power     for(int i = 1; i <= N; i++)     {         S += i * i * i * i;     }       // Return the average     return S / N; }   // Driver code public static void main(String[] args) {     int N = 3;       System.out.println(findAverage(N)); } }   // This code is contributed by abhinavjain194

## Python3

 # Python3 program for the above approach   # Function to find the average of the # fourth power of first N natural numbers def findAverage(N):       # Stores the sum of the fourth     # powers of first N natural numbers     S = 0       # Calculate the sum of fourth power     for i in range(1, N + 1):         S += i * i * i * i       # Return the average     return round(S / N, 4)   # Driver Code if __name__ == '__main__':           N = 3     print(findAverage(N))   # This code is contributed by mohit kumar 29

## C#

 // C# program for the above approach using System;   class GFG{   // Function to find the average of the // fourth power of first N natural numbers static double findAverage(int N) {           // Stores the sum of the fourth     // powers of first N natural numbers     double S = 0;        // Calculate the sum of fourth power     for(int i = 1; i <= N; i++)     {         S += i * i * i * i;     }        // Return the average     return S / N; }       // Driver Code public static void Main() {     int N = 3;           Console.WriteLine(findAverage(N)); } }   // This code is contriobuted by sanjoy_62

## Javascript

 

Output:

32.6667

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

Efficient Approach: The above approach can also be optimized by finding the sum of the fourth powers of the first N natural numbers by the mathematical formula given below and then print its value when divided by N.

The mathematical formula is as follows:

=> => => Below is the implementation of the above approach:

## C++

 // C++ program for the above approach   #include  using namespace std;   // Function to find the average of the // fourth power of first N natural numbers double findAverage(int N) {     // Store the resultant average     // calculated using formula     double avg = ((6 * N * N * N * N)                   + (15 * N * N * N)                   + (10 * N * N) - 1)                  / 30.0;       // Return the average     return avg; }   // Driver Code int main() {     int N = 3;     cout << findAverage(N);       return 0; }

## Java

 // Java program for the above approach import java.util.*;   class GFG{       // Function to find the average of the // fourth power of first N natural numbers static double findAverage(int N) {           // Store the resultant average     // calculated using formula     double avg = ((6 * N * N * N * N) +                  (15 * N * N * N) +                   (10 * N * N) - 1) / 30.0;       // Return the average     return avg; }   // Driver Code public static void main(String args[]) {     int N = 3;           System.out.print(findAverage(N)); } }   // This code is contributed by shivanisinghss2110

## Python3

 # Python program for the above approach   # Function to find the average of the # fourth power of first N natural numbers def findAverage(N):           # Store the resultant average     # calculated using formula     avg = ((6 * N * N * N * N) + (15 * N * N * N) + (10 * N * N) - 1) / 30           # Return the average     return avg   N = 3 print(round(findAverage(N),4))         # This code is contributed by avanitrachhadiya2155

## C#

 // C# program for the above approach using System;   class GFG{       // Function to find the average of the // fourth power of first N natural numbers static double findAverage(int N) {           // Store the resultant average     // calculated using formula     double avg = ((6 * N * N * N * N) +                  (15 * N * N * N) +                   (10 * N * N) - 1) / 30.0;       // Return the average     return avg; }   // Driver Code public static void Main() {     int N = 3;     Console.WriteLine(findAverage(N)); } }   // This code is contributed by ukasp

## Javascript

 

Output:

32.6667

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

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