Any of the series of numbers (1, 3, 6, 10, 15, etc.) obtained by continued summation of the natural numbers 1, 2, 3, 4, 5, etc.

What are Triangular Numbers?
Triangular numbers are a special set of numbers that can be arranged in the shape of an equilateral triangle. They are formed by the sum of the natural numbers up to a certain point.

Definition
- Triangular numbers represent the total number of dots that can form a triangle.
- The nth triangular number is the sum of the first n natural numbers.

Formula
- The formula to find the nth triangular number is:
T(n) = n(n + 1) / 2
where T(n) is the nth triangular number.

Examples
- The first few triangular numbers are:
- T(1) = 1
- T(2) = 1 + 2 = 3
- T(3) = 1 + 2 + 3 = 6
- T(4) = 1 + 2 + 3 + 4 = 10
- T(5) = 1 + 2 + 3 + 4 + 5 = 15

Visual Representation
- These numbers can be visualized as:
- T(1): ●
- T(2):
●
● ●
- T(3):
●
● ●
● ● ●
- T(4):
●
● ●
● ● ●
● ● ● ●

Applications
- Triangular numbers appear in various areas of mathematics and can be used in solving problems involving arrangements, combinations, and patterns.
Understanding triangular numbers provides a foundational insight into number theory and shapes, making them an exciting topic in mathematics for students!