Use the triangular numbers tool below to calculate the triangular number of any given number. Find below in this web page a triangular numbers list from 1 to 100 as well as the nth term formula as well as its demonstration.
What are triangular numbers?
A triangular number or triangle number counts the objects that can form an equilateral triangle. The nth triangle number is the number of dots composing a triangle with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n.
The general representation of a triangular number is
Tn= 1 + 2 + 3 + 4 +...+ (n-2) + (n-1) + n,
where n is a natural number.
This sum is Tn = n * (n + 1) / 2. This is the triangular number formula to find the nth triagular number.
To prove that this formula is true, write twice the general representation and rearange the terms as below