Sum of N Natural Numbers (JavaScript)

Calculating the sum of the first N natural numbers is a classic problem in programming and mathematics. Natural numbers are positive integers (1, 2, 3, …). This problem helps to understand basic arithmetic operations and loop usage in JavaScript.

The goal is to add all the positive integers from 1 up to a given number ‘N’. For example, if N is 5, the sum would be 1 + 2 + 3 + 4 + 5 = 15.

This is a straightforward method where you iterate from 1 to N, accumulating the sum.

Explanation:

• totalSum is initialized to 0.
• The for loop iterates from 1 to limitN.
• In each iteration, the current number is added to totalSum.

There's a well-known mathematical formula for the sum of the first N natural numbers, attributed to Gauss: Sum = N * (N + 1) / 2. This method is highly efficient for large values of N as it avoids iteration.

Explanation:

• The formula is directly applied to limitN.
• This method is much faster for larger N as it doesn't require a loop.

• Iterative vs. Formulaic Solutions: Understanding when to use a loop and when a direct formula is more efficient.
• Arithmetic Series: The sum of natural numbers is an example of an arithmetic series.
• Efficiency: The formulaic approach is significantly more efficient for large N compared to the iterative approach due to its constant time complexity (O(1)).