We have discussed how Gauss was able to devise a clever way to add the first 
positive integers at a very young age in a few minutes. We generalized his method and have also seen the link between the sum and the area of a triangle. In both discussions, we have shown that the sum of the first 
positive integers is 
.
In this post, we discuss another geometric proof of the problem above. We start with a specific case adding the first 
positive integers, and the proceed to the general case.
We can add the first positive integers manually or just by counting the number of unit squares in the figure above. The figure shows the geometric representation of the sum of the first 6 positive integers. Adding manually is not difficult if the given is small. However, we need a strategy for larger numbers. » Read more