Discovering the Magic of Triangular Numbers: A Simple Formula
Numbers have a way of surprising us with their patterns, and one such fascinating pattern emerges from triangular numbers. If you’ve ever stacked objects in the shape of a triangle or wondered how adding up consecutive natural numbers works, this is where triangular numbers come in. In this post, we’ll walk through a simple yet powerful method to find the sum of the first 20 natural numbers using this triangular number formula. Ready to uncover some mathematical magic? Let’s dive in! --- ### What Are Triangular Numbers? Triangular numbers are a sequence of numbers that can be represented as dots arranged in the shape of a triangle. For example, the number 3 can be visualized as a triangle made up of two rows—one row with 2 dots and another row with 1 dot. The general formula to calculate the sum of the first *n* natural numbers (which gives us the *n*th triangular number) is: \[ S_n = \frac{n(n+1)}{2} \] Here, \( S_n \) represents the sum of the first *n* numbers. Essentially, it take