# Triangular Numbers

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Meets NCTM Standards:
Lesson Summary:

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.

Lesson Description:

An introduction to triangular numbers.

• What are triangular numbers?
• How do you find triangular numbers?
• How can you compute the nth triangular number?
• How did Gauss find the sum of natural numbers from 1 to 100?
• #### Staff Review

• Currently 3.0/5 Stars.
This is a very basic video about triangular numbers, but the visuals help show them in a meaningful way. To find any triangular number, the video explains finding the sum of all natural numbers from 1 to n using a method that Gauss found. This historical anecdote is also explained.
• #### Aishah

• Currently 4.0/5 Stars.
good it was okay but could be better thanks