I would say it's not as interesting because a high-schooler (or Pythagoras) could easily verify the fact AND they would easily be able to explain how you came

I would say it's not as interesting because a high-schooler (or Pythagoras) could easily verify the fact AND they would easily be able to explain how you came up with that sum. One of my metrics for determining if a fact F is interesting is if P(F) is much larger than V(F). Here P(F) is, vaguely speaking, the amount of effort required to "explain" or "generalize" the fact, and V(F) is the amount of effort required to verify the fact. In the case of e^{-x}, each individual example can be verified by an elementary schooler so V(F) is very small. On the other hand, I don't see how you could explain the phenomena of convergence to 0 without teaching the elementary schooler a large part of calculus, so P(F)/V(F) is large.