Triangular Numbers: Sum of the First N Positive Integers - Formulas and Reasoning
One important summation fact involves taking the sum of the positive integers starting with 1 and ending with a positive integer we choose, which I will call N. This sum is called the N'th Triangular number, because we can represent the sum as a stack of boxes diagram that looks like a traingle. The formula for simplifying this sum is pretty straightforward, it is equal to N*(n+1)/2. I will show two ways that we could figure out this formula, so you will know where it comes from and aren't just memorizing random symbols.
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