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 = 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:

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:

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Below is the implementation of the above approach:

32.6667

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