The recursive case is where you break the problem into a smaller version of itself. You assume you can solve the smaller problem, then use that solution to build the answer for the current problem.
For example, to compute , you say "if I knew , then ". This "leap of faith" is the key to recursion: you trust that the recursive call will work, even though you are still writing the function.
I was personally amused when I first saw this. How can you call something that does not exist yet? It feels magical, doesn't it? But it works because each call handles a smaller piece. The recursive call always moves you closer to the base case.
