I'm the one that's missing something regarding you changing it.
"Before entering on an understanding, I have meditated for a long time, and have foreseen what might happen. It is not genius which reveals to me suddenly, secretly, what I have to say or to do in a circumstance unexpected by other people; it is reflection, it is meditation." - Napoleon I
I would however presume that if the teacher is teaching recursion and then assigns the above problem then the teacher is going to expect a code that does recursion. Whether it causes a stack overflow is outside the bounds of what the teacher is teaching. Although perhaps a teacher that is clever (or trying to be clever) might even provide inputs that would cause an overflow just so the students would need to fumble about with that.
I don't understand your response in terms of what they could figure out?
I know that when I first learned recursion that it took about 12/18 months for me to get it after I was first taught it. I remember it specifically because I had a very 'aha' moment studying late a night when I finally understood it.
Anyone who seriously considers this problem for a recursive solution must be one who has just recently learned about recursion and thinks of it as a universal cure for all the ills of the programming world.
(Any 'for' loop can easily be rewritten to a recursive solution!)
But if it's a homework assignment to teach the student about recursion, as jschell suggested...
... it is a very poor choice.
When teaching, I did give my students a recursive problem statement to solve. Most of the solutions were recursive. The main point of this exercise was to, in the next round, show how some recursions could be rolled out to loops; the problem statement was selected for this specific purpose: Learning when not to use recursion, even when it looks like the straightforward, obvious solution.
I never wold give my students a 'linear' problem statement (such as the one in the subject line), hoping that they would discover 'Hey, this iteration can be reformualated as a recursive method! Let's do that!'
If I were a teacher of higher math, I might use something in that direction to teach them to identify recursive structures. But I was a programming teacher. That is very different.
Anyone who seriously considers this problem for a recursive solution
As I said "Looks like homework for recursion.."
But with my 40 years of development experience and numerous cases of recursion unrolling not to mention more than 30 years of formal designs and 20 of architecture...
Myself I would probably start by looking at the requirements to see why either solution was needed. Certainly in the past I have, after using all that experience, decided that a simple look up in a static data block would completely meet the needs of the application/requirements.
And of course that solution would be much more efficient than recursion or the similar unrolled version. In case you were unaware of that.
If you teach recursion to students, you should illustrate it, and create homework assignments, with problems suited for recursion.
Students should not, through inappropriate homework assignments, learn to use the wrong tools for the problem at hand.
So if that is the case here, the teacher should be blamed. Especially if the assignment is as suggested in the subject line, with no hint of recursion in the problem statement. A lot of problems can be described in a very concise form in recursive terms, but can easily be implemented as an iteration (and most students will not discover that and make a recursive implementation ... I speak of experience). Here is no trace of a recursive problem description.
and create homework assignments, with problems suited for recursion.
Not sure what you mean.
First of course teachers are human. So like any other group there a good ones, bad ones and a whole lot of average ones. So yes they might be using a bad example.
Second I can see where the equation can be solved by recursion. Probably too complicated both for teaching recursion and for teaching other methods as well. Although perhaps the class will also include unrolling and perhaps then it might be better (hypothetically of course.) And then perhaps the teacher feels that would be a good follow on from this specific example.
So if that is the case here, the teacher should be blamed. Especially if the assignment is as suggested in the subject line,
Quite possibly. But then what is the scenario where that specific equation is an effective tool for teaching the basics of say a 'for' loop.
Are you claiming it is a good example for that?
Or are you claiming that the teacher is still bad but in fact must be teaching about loops instead?
A lot of problems can be described in a very concise form in recursive terms, but can easily be implemented as an iteration (and most students will not discover that and make a recursive implementation ... I speak of experience). Here is no trace of a recursive problem description.
There is a lot in that.
First in my experience classroom work, never, teaches the use of the field in practical terms. Not in programming, not in engineering, not in the soft sciences, etc.
Not even in the field of teaching. One possible exception might be that if one wants to learn to be a university professor. And only a university professor. But not for example a middle school teacher.
Possible it has changed since I was in school but I haven't run into any young programmers that even know what bit fiddling is. So I doubt it.
Second, as I remember, university professors did like recursion quite bit. Probably because, as you noted, the expression is concise. They were using it to teach the algorithm and not, as I noted above, practical programming. So in that case it doesn't matter if the implementation would be impractical.