Sum of First N Positive Integers: Formula & Triangular Number Explanation

This expression represents the sum of the first 'n' positive integers. It is also known as the 'n'th triangular number, because if you represent each integer as a dot and arrange them in a triangular pattern, this expression gives you the total number of dots. For example, the fourth triangular number is (\frac{4(4+1)}{2}=10), which you can represent as a triangle with four rows:

$$\begin{matrix}\cdot\cdot \quad \cdot\cdot \quad \cdot \quad \cdot\cdot \quad \cdot \quad \cdot \quad \cdot\end{matrix}$$