Sum of first n natural numbers (How?)

Thought provoking

In my earlier blog “Sum of first n natural numbers”, my question was, How did one arrived with the formula to calculate sum of first “n” natural numbers, “n * (n+1)/2)”. Some of the readers made me realize that I ended by up writing “how to prove the formula”. Here I am re-organizing visuals to show how it can be thought provoking.

Our problem is to find value of 1 + 2 + 3 + 4 +… +n. For the illustration consider n =4.

Some people has that intuition to identify the patterns and come up with formulae.