# Mean of fourth powers of first N natural numbers

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 = 3Output:32.6667Explanation:

The sum of the fourth powers of the first N natural numbers = 1^{4 }+ 2^{4}+ 3^{4}= 1 + 16 + 81 = 98.

Therefore, the average = 98 / 3 = 32.6667.

Input:N = 5Output: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 <bits/stdc++.h>` `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

`<script>` `// javascript program for the above approach` `// Function to find the average of the` `// fourth power of first N natural numbers` `function` `findAverage(N)` `{` ` ` `// Stores the sum of the fourth` ` ` `// powers of first N natural numbers` ` ` `var` `S = 0;` ` ` ` ` `var` `i;` ` ` `// Calculate the sum of fourth power` ` ` `for` `(i = 1; i <= N; i++) {` ` ` `S += i * i * i * i;` ` ` `}` ` ` `// Return the average` ` ` `return` `S / N;` `}` `// Driver Code` ` ` `var` `N = 3;` ` ` `document.write(findAverage(N));` `</script>` |

**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 <bits/stdc++.h>` `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

`<script>` ` ` `// JavaScript program for the above approach` `// Function to find the average of the` `// fourth power of first N natural numbers` `function` `findAverage( N)` `{` ` ` `// Store the resultant average` ` ` `// calculated using formula` ` ` `let avg = ((6 * N * N * N * N)` ` ` `+ (15 * N * N * N)` ` ` `+ (10 * N * N) - 1)` ` ` `/ 30.0;` ` ` `// Return the average` ` ` `return` `avg;` `}` `// Driver Code` ` ` `let N = 3;` ` ` `document.write( findAverage(N).toFixed(4));` `// This code is contributed by G.Sravan Kumar (171FA07058)` `</script>` |

**Output:**

32.6667

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

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