As usual, the "..." represents infinitely many copies
of the square-root-of-two-plus operation.
This definitely counts as an "Aha" problem, in the
sense that typical high-school students think this is
a hard problem -- infinitely hard, in fact -- and are
intimidated by it ... yet when they see the answer
they can understand it.
I like this question for several reasons. For one thing,
it makes a good "Here's why you go to school" story:
this looks like a hard problem now, but if you learn how
to think properly about such things, this will become
so easy you can solve it in less time than it takes to
talk about it. The infinity actually makes it easier;
the infinite version is easier than most of the finite
(but large) problems from the same family.
Another nice thing is that the problem can be solved
in two rather different ways. Looking at something
in two different ways is always good exercise for the
thinking muscle.
It also serves as a reminder that calculus class was
supposed to teach more than just derivatives and integrals.
Last but not least, I can think of at least two interesting
physics applications for the sort of reasoning involved
here:
-- renormalization group, which allows us to understand
phase transitions and critical phenomena, and
-- iterated nonlinear maps show up a lot in connection
with chaos and turbulence.