Recursion with Triangle Numbers

Here are the two parts to recursion:

1. If the problem is easy, solve it immediately.
   • An easy problem is a base case.
2. If the problem can't be solved immediately, divide it into smaller problems, then:
   • Solve the smaller problems by applying this procedure to each of them.

And here is how this applies to triangle numbers:

1. Triangle( 1 ) = 1
2. Triangle( N ) = N + Triangle( N-1 )

The problem "Triangle(N)" is divided into two problems: "add N to something" and "Triangle(N-1)". Sometimes the latter can be solved immediately (when it is the base case). Other times you need to re-apply the solution to the smaller problem.