IF YOU ARRANGE 15 DOTS in the shape of a triangle, you end up with an arrangement that might look something like this:
•• •• • •• • • •• • • • •
The first row of the triangle contains one dot, the second row contains two dots, and so on. In general, the number of dots it takes to form a triangle containing n rows is the sum of the integers from 1 through n. This sum is known as a triangular number. If you start at 1, the fourth triangular number is the sum of the consecutive integers 1 through 4 (1 + 2 + 3 + 4), or 10.
Suppose you want to write a program that calculates and displays the value of the eighth triangular number at the terminal. Obviously, you could easily calculate this number in your head, ...