The triangular numbers are the numbers which are the sum of the first natural numbers from to .
The triangular number is the sum of all natural numbers from one ton. That is, the triangle number is .
For example, the first few triangular numbers can be calculated by adding 1, 1+2, 1+2+3, ... etc. giving the first few triangular numbers to be .
A rather simple recursive definition can be found by noting that .
They are called triangular because you can make a triangle out of dots, and the number of dots will be a triangular number:
Using the sum of an arithmetic series formula, a formula can be calculated for :
The formula for finding the triangular number can be written as .
It can also be expressed as the sum of the row in Pascal's Triangle and all the rows above it. Keep in mind that the triangle starts at Row 0.
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