In this lesson, we learn about triangular numbers and how they relate to the sum of consecutive natural numbers. The first three triangular numbers are 1, 3, and 6, and we can find the nth triangular number by adding the first n natural numbers. We also learn about a shortcut for finding the sum of the first n natural numbers, discovered by the famous mathematician Carl Friedrich Gauss, who realized that when you add pairs of numbers from the beginning and end of the sequence, the sum remains constant. Applying this, he was able to quickly and easily find the sum of the first 100 natural numbers.
An introduction to triangular numbers.