Final answer:
The answer to the fill-in-the-blank question is 'base cases.' These are critical for ensuring that a recursive method terminates and doesn't lead to an infinite loop or stack overflow error. Recursive methods can call themselves directly or indirectly and need at least one base case to stop the recursion.
Step-by-step explanation:
A recursive method is a method that invokes itself directly or indirectly. For a recursive method to terminate there must be one or more base cases.
Recursion is a programming concept where a function calls itself to solve a smaller instance of the original problem, and this process repeats until it reaches a condition that prevents further recursion — the base case. Without a base case, a recursive method may lead to infinite recursion and potentially a stack overflow error. Thus, the base case acts as the stopping condition that ensures recursion ends once the desired state is achieved or the problem is solved.