A natural number is called TRIANGULAR when it is obtained by adding all positive integers less than or equal to a given positive integer.

For example:

10 e 15 are triangular numbers because 10=1+2+3+4 15=1+2+3+4+5

Triangular numbers are also called figurate  numbers because they can be represented in this way:

or

PROPERTIES

A triangular number can be calculated with Gauss formula:

nx(n+1)/2

For example:

10= 1+2+3+4= 4x5/2