The triangular numbers are the numbers which are the sum of the first natural numbers from to .
Using the sum of an arithmetic series formula, a formula can be calculated for :
For example, the triangle number is
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.
The rather simple recursive definition can be easily found by noting that .
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