Here is the answer to questions like: Triangular numbers of 247 or what is 247 triangular number?
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