Triangular Numbers & Sums of Sequences
1954 views
|
1
rating
Lesson Summary:
In this lesson, you will learn about triangular numbers and their geometric interpretation. By arranging stones in equilateral triangular shapes, you can easily count the number of stones and produce triangular numbers. You will also see how the sum of two consecutive triangular numbers results in a square number, and learn how to solve recurrence equations to find the end triangular number. These easy solutions provide insight into some other mathematical topics, making the discovery of elementary results accessible to all.
Lesson Description:
Learn how to generalize a sequence and find related sums by using triangular numbers and their geometric interpretation.
Questions answered by this video:
- How can you find the nth triangular number geometrically?
- Why is the sum of two consecutive triangular numbers equal to a square number?
- How are triangular and square numbers related?
- What is abstraction?
- What is generalization?
-
Staff Review
This video explains some very interesting geometrical and algebraic properties of triangular and square numbers. It shows a geometrical way of thinking about computing these numbers. Then, this video explains how sequences are generalized and how their sums can be found.
