Tuesday, April 10, 2012

On Triangular Numbers...

Any number whose units form an equilateral triangle is called a triangular number.
It's not just that.
You chop off any side of the triangle thus formed, you still get a triangular number.
They're 1,3,6,10,15,21,... There is no end to this list. It goes to infinity.
Wonderful are the properties of triangular numbers.
Now, take any number n, multiply it with 2n+1, it's a triangular number.
Suppose by mistake you put the sign as - instead of +, you still get a triangular number.
If n is odd, then the product is an odd triangular number and if n is even, then you'll get an even triangular number.
Hence, the entire triangular number sequence can be obtained as follows:
n x (2n-/+1), where n=1,2,3,4,...