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.

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1 + 2 + 3+ 4 + 5 = 5 * (5+1)/2 = 15

Today morning I woke up with the question, how did one arrived with the formula to calculate sum of first “n” natural numbers, “n * (n+1)/2)”. I messaged my friends, some referred me to arithmetic series and some to “Triangular Number”. I recollected that I learnt arithmetic series approach in school but never came across triangular numbers. While reading about triangular number I came across “visual proof/proof without words”. I like the approach and demonstrating it below.

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