That was literally what the professor teaching us recursion in college would say “trust your recursion”. Using factorial as the example, you know n! = n(n-1)!. Translating to code, you end up with

# python, for example
def fact(n):
    if n == 0:
        return 1
    else:
        return n * ???

You need something to compute (n-1)! Well, that would be fact(n-1), if it worked, so trust that it does.

I think it’s a little easier to segue into this when you have first-class functions. You can pass the problem on to caller, so to speak. For example:

def fact(n, helper):
    if n == 0:
        return 1
    else:
        return n * helper(n-1)

If you don’t know how to compute (n-1)!, just make the caller provide a function to do it for you. Then the caller, face with finding 7!, might write

fact(7,

then look around for a suitable helper, and decide that, well, fact(6) should work, let’s try fact(7, fact), and lo and behold, it does work.

But if the caller always uses the “fact(n, fact)” trick, you may as well hardcode it, turning the nonrecursive definition into the desired recursive definition.